slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · slide 9 / 53...
TRANSCRIPT
![Page 3: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/3.jpg)
Slide 3 / 53
Topics Table of ContentsClick on a topic to go to that sectionDetermining if a Triangle is Possible
Geometric Constructions: The Basics
Videos Table of ContentsVideos Using Geometer's Sketchpad
Video: Constructing Circles
Video: Constructing Isosceles Triangles
Video: Constructing Equilateral Triangles
Video: Congruent Triangles
Glossary
![Page 4: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/4.jpg)
Slide 3 (Answer) / 53
Topics Table of ContentsClick on a topic to go to that sectionDetermining if a Triangle is Possible
Geometric Constructions: The Basics
Videos Table of ContentsVideos Using Geometer's Sketchpad
Video: Constructing Circles
Video: Constructing Isosceles Triangles
Video: Constructing Equilateral Triangles
Video: Congruent Triangles
Glossary
[This object is a pull tab]
Teac
her N
otes
Constructions are shown within the lesson using paper and pencil. There are also video links showing how to do the constructions using Geometer's Sketchpad. A free version of this program is available at:
http://info.mheducation.com/sketchpad.trial.html
![Page 6: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/6.jpg)
Slide 5 / 53
How many different acute triangles can you draw?
How many different right scalene triangles can you draw?
Recall that triangles can be classified according to their side lengths and the measure of their angles.
Sides:Scalene - no sides are congruentIsosceles - two sides are congruentEquilateral - all three sides are congruent
Angles:Acute - all three angles are acuteRight - contains one right angleObtuse - contains one obtuse angle
Drawing Triangles
![Page 7: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/7.jpg)
Slide 6 / 53
There is another property that applies to triangles:
Click the lab below to determine what the Triangle Inequality Property is about.
Triangle Inequality Lab
Triangle Inequality Property
![Page 8: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/8.jpg)
Slide 7 / 53
Triangle Inequality: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
What does this mean?
If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side.
If that is not true, then it is not possible to construct a triangle with the given slide lengths.
Triangle Inequality Property
![Page 9: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/9.jpg)
Slide 8 / 53
ExampleDetermine if sides of length 5 cm, 8 cm and 12 cm can form a triangle?
Test all three pairs to see if the sum is greater:5 + 8 > 12 5 + 12 > 8 8 + 12 > 5 13 > 12 17 > 8 20 > 5
Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.
![Page 10: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/10.jpg)
Slide 9 / 53
ExampleDetermine if sides of length 3 ft, 4 ft and 9 ft can form a triangle?
Test all three pairs to see if the sum is greater:3 + 4 > 9 3 + 9 > 4 4 + 9 > 3 7 > 9 12 > 4 13 > 3
No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.
![Page 11: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/11.jpg)
Slide 10 / 53
Try TheseDetermine if triangles can be formed with the following side lengths:
1. 4 cm, 7 cm, 10 cm 2. 24 mm, 20 mm, 30 mm
4 + 7 > 10 24 + 20 > 30 4 + 10 > 7 24 + 30 > 20 7 + 10 > 4 20 + 30 > 24 YES YES
3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in
7 + 9 = 16 9 + 13 < 24 7 + 16 > 9 9 + 24 > 13 16 + 9 > 7 13 + 24 > 9 NO NO
![Page 12: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/12.jpg)
Slide 11 / 53
1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work!
YesNo
![Page 13: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/13.jpg)
Slide 11 (Answer) / 53
1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work!
YesNo
[This object is a pull tab]
Ans
wer
No
![Page 14: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/14.jpg)
Slide 12 / 53
2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work!
YesNo
![Page 15: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/15.jpg)
Slide 12 (Answer) / 53
2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work!
YesNo
[This object is a pull tab]
Ans
wer
Yes
![Page 16: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/16.jpg)
Slide 13 / 53
3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work!
YesNo
![Page 17: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/17.jpg)
Slide 13 (Answer) / 53
3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work!
YesNo
[This object is a pull tab]
Ans
wer
No
![Page 18: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/18.jpg)
Slide 14 / 53
4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work!
YesNo
![Page 19: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/19.jpg)
Slide 14 (Answer) / 53
4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work!
YesNo
[This object is a pull tab]
Ans
wer
No
![Page 20: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/20.jpg)
Slide 15 / 53
5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work!
YesNo
![Page 21: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/21.jpg)
Slide 15 (Answer) / 53
5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work!
YesNo
[This object is a pull tab]
Ans
wer
Yes
![Page 22: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/22.jpg)
Slide 16 / 53
6 A triangle could have which of the following sets of angles?
A 40º, 90º, 105º
B 35º, 89º, 56º
C 75º, 90º, 15º
D 30º, 65º, 95º
![Page 23: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/23.jpg)
Slide 16 (Answer) / 53
6 A triangle could have which of the following sets of angles?
A 40º, 90º, 105º
B 35º, 89º, 56º
C 75º, 90º, 15º
D 30º, 65º, 95º [This object is a pull tab]
Ans
wer
B
![Page 24: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/24.jpg)
Slide 17 / 53
7 A triangle could have which of the following sets of angles?
A 37º, 63º, 80º
B 90º, 104º, 76º
C 23º, 47º, 50º
D 80º, 90º, 10º
![Page 25: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/25.jpg)
Slide 17 (Answer) / 53
7 A triangle could have which of the following sets of angles?
A 37º, 63º, 80º
B 90º, 104º, 76º
C 23º, 47º, 50º
D 80º, 90º, 10º
[This object is a pull tab]
Ans
wer
A, D
![Page 26: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/26.jpg)
Slide 18 / 53
ExamplePredict the length of the third side of a triangle with sides of length 12 ft and 16 ft.
Side 1 = 12 ftSide 2 = 16 ft
The 3rd side must be less than: 12 + 16 > 3rd side 28 ft > 3rd side
The 3rd side must be greater than: 12 + 3rd side > 16 3rd side > 4
The 3rd side must be greater than 4 ft and less than 28 ft.
![Page 27: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/27.jpg)
Slide 19 / 53
ExamplePredict the length of the third side of a triangle with sides of length 9 cm and 15 cm.
Side 1 = 9 cmSide 2 = 15 cm
The 3rd side must be less than: 9 + 15 > 3rd side 24 cm > 3rd side
The 3rd side must be greater than: 9 + 3rd side > 15 3rd side > 6
The 3rd side must be greater than 6 cm and less than 24 cm.
![Page 28: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/28.jpg)
Slide 20 / 53
Try ThesePredict the length of the third side of a triangle whose known sides are lengths:
1. 13 mm, 20 mm 2. 7 in, 19 in
13 + 20 > Side 3 7 + 19 > Side 3 33 > Side 3 26 > Side 3
13 + Side 3 > 20 7 + Side 3 > 19 Side 3 > 7 Side 3 > 12
7 < side 3 < 33 12 < side 3 < 26
![Page 29: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/29.jpg)
Slide 21 / 53
Try ThesePredict the length of the third side of a triangle whose known sides are lengths:
3. 4 ft, 11 ft 4. 23 cm, 34 cm
4 + 11 > Side 3 23 + 34 > Side 3 15 > Side 3 57 > Side 3
4 + Side 3 > 11 23 + Side 3 > 34 Side 3 > 7 Side 3 > 11
7 < side 3 < 15 11 < side 3 < 57
![Page 30: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/30.jpg)
Slide 22 / 53
8 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.
![Page 31: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/31.jpg)
Slide 22 (Answer) / 53
8 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.
[This object is a pull tab]
Ans
wer
6 m
![Page 32: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/32.jpg)
Slide 23 / 53
9 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.
![Page 33: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/33.jpg)
Slide 23 (Answer) / 53
9 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m.
[This object is a pull tab]
Ans
wer
18 m
![Page 34: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/34.jpg)
Slide 24 / 53
10 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.
![Page 35: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/35.jpg)
Slide 24 (Answer) / 53
10 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.
[This object is a pull tab]
Ans
wer
8 in
![Page 36: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/36.jpg)
Slide 25 / 53
11 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.
![Page 37: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/37.jpg)
Slide 25 (Answer) / 53
11 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in.
[This object is a pull tab]
Ans
wer
26 in
![Page 38: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/38.jpg)
Slide 26 / 53
12 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.
![Page 39: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/39.jpg)
Slide 26 (Answer) / 53
12 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.
[This object is a pull tab]
Ans
wer
28 ft
![Page 40: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/40.jpg)
Slide 27 / 53
13 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.
![Page 41: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/41.jpg)
Slide 27 (Answer) / 53
13 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft.
[This object is a pull tab]
Ans
wer
58 ft
![Page 43: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/43.jpg)
Slide 29 / 53
In Geometry, we can draw just about every figure with various tools. The tools that we will be using are given on this slide & the next slide:
1) Compass : creating circles & arcs
Geometric Tools
![Page 44: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/44.jpg)
Slide 29 (Answer) / 53
In Geometry, we can draw just about every figure with various tools. The tools that we will be using are given on this slide & the next slide:
1) Compass : creating circles & arcs
Geometric Tools
[This object is a pull tab]
Teac
her N
otes
Show the students how the compass works by rotating it to form a circle.
![Page 45: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/45.jpg)
Slide 30 / 53
2) Ruler : measure segmentsD E DE = 6 cm
B C
A
m∠ABC = 65°
3) Protractor: measure angles
Geometric Tools
![Page 46: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/46.jpg)
Slide 31 / 53
Example Draw a circle that has a radius of 6 cm.
Step #1: Draw a segment w/ the ruler that measures 6 cm.
Step #2: Line up your compass so that it's center tip lies on one endpoint & the pencil tip lies on the other endpoint.
![Page 47: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/47.jpg)
Slide 32 / 53
Step #3: Keeping the distance between the center & endpoint the same, draw your circle.
![Page 48: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/48.jpg)
Slide 32 (Answer) / 53
Step #3: Keeping the distance between the center & endpoint the same, draw your circle.
[This object is a pull tab]
Teac
her N
otes It might help to hold
the compass firmly in place & rotate the paper beneath the compass.
![Page 49: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/49.jpg)
Slide 33 / 53
Try this!1) Construct a Circle that has a radius of 3 cm using a ruler & a compass.
![Page 50: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/50.jpg)
Slide 33 (Answer) / 53
Try this!1) Construct a Circle that has a radius of 3 cm using a ruler & a compass.
[This object is a pull tab]
Teac
her N
otes
Circulate around the room to make sure that the students are constructing the circles correctly. Figures should resemble the figure below.
3 cm
![Page 51: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/51.jpg)
Slide 34 / 53
Try this!2) Construct a Circle that has a radius of 8 cm using a ruler & a compass.
Video: Constructing Circles
![Page 52: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/52.jpg)
Slide 34 (Answer) / 53
Try this!2) Construct a Circle that has a radius of 8 cm using a ruler & a compass.
Video: Constructing Circles
[This object is a pull tab]
Teac
her N
otes
Circulate around the room to make sure that the students are constructing the circles correctly. Figures should resemble the figure below.
8 cm
![Page 53: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/53.jpg)
Slide 35 / 53
A B
Example Use a ruler & a compass to draw an isosceles triangle w/ the following conditions: 1. at least one of the sides is 7 cm 2. at least one of the sides is 3 cm
Step #1: Look at your conditions. Both of them say "at least one" which means that one side, or more sides could meet the conditions. Plus, since the triangle is isosceles, we know that two of the sides must be equal. So pick which number you want to occur for 2 of your sides.
I'll select the 7 cm to occur twice.
Step #2: Draw one of your 7 cm segments.
![Page 54: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/54.jpg)
Slide 36 / 53
A B
Step #3: With your compass, draw a circle or semicircle (whichever you prefer).
Any segment that I connect from this arc to the center will have the same radius length of 7 cm.
![Page 55: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/55.jpg)
Slide 37 / 53
Step #4: With your ruler, find the segment that can be drawn from B to another point on the semicircle so that the ruler measures 3 cm. Make a point at this location.
A B
Step #5: Connect this point with points A & B to form your triangle.
A B
C
Note: AC = AB = 7 cm, since they are both radii of the circle.
![Page 56: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/56.jpg)
Slide 38 / 53
Think about this...
Can we make a triangle if we use the 3 cm twice and the 7 cm once?
Discuss this problem in your groups for a few minutes.
![Page 57: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/57.jpg)
Slide 38 (Answer) / 53
Think about this...
Can we make a triangle if we use the 3 cm twice and the 7 cm once?
Discuss this problem in your groups for a few minutes.
[This object is a pull tab]
Ans
wer
No:3 + 3 > 76 > 7
?
![Page 58: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/58.jpg)
Slide 39 / 53
Try this!3) Use a ruler & a compass to draw an isosceles triangle w/ the following conditions: 1. at least one of the sides is 8 cm 2. at least one of the sides is 6 cm
Video: Constructing Isosceles Triangles
![Page 59: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/59.jpg)
Slide 39 (Answer) / 53
Try this!3) Use a ruler & a compass to draw an isosceles triangle w/ the following conditions: 1. at least one of the sides is 8 cm 2. at least one of the sides is 6 cm
Video: Constructing Isosceles Triangles
[This object is a pull tab]
Ans
wer
Circulate around the room to make sure that the students are constructing the triangle correctly. Note: 2 answers (could ask them to find both for extra practice): 8 cm, 8 cm & 6 cm & 6 cm, 6 cm & 8 cm
8 cm
8 cm
6 cm
6 cm
6 cm
8 cm
![Page 60: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/60.jpg)
Slide 40 / 53
Example Use a ruler & a protractor to draw an equilateral triangle that has a side length of 5.5 cm.
Step #1: Reread your question. We have an equilateral triangle, which has all of the sides measuring 5.5 cm & all of its angles measure to be 60°.
Step #2: Draw one of your 5.5 cm segments.
C D
![Page 61: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/61.jpg)
Slide 41 / 53
C D
Step #2: With your protractor, place its center at either point C or point D (doesn't matter), measure 60° & draw a line connecting the 60° measurement with your center (mine is C).
Step #3: Repeat step #2 with your other endpoint as the center.
C D
![Page 62: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/62.jpg)
Slide 42 / 53
C D
Step #4: Draw a point where the 2 lines intersect & erase any additional lines.
Note: You can verify that all of the edges are equal by measuring all of them.
![Page 63: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/63.jpg)
Slide 43 / 53
Try this!4) Construct an equilateral triangle that has a side length of 4.2 cm using a protractor and a ruler.
![Page 64: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/64.jpg)
Slide 43 (Answer) / 53
Try this!4) Construct an equilateral triangle that has a side length of 4.2 cm using a protractor and a ruler.
[This object is a pull tab]
Ans
wer
Circulate around the room to make sure that the students are constructing the triangles correctly. Diagrams should resemble the figure below.
4.2 cm
4.2 cm4.2 cm
![Page 65: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/65.jpg)
Slide 44 / 53
Try this!5) Construct an equilateral triangle that has a side length of 6.7 cm using a protractor and a ruler.
Video: Constructing Equilateral Triangles
![Page 66: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/66.jpg)
Slide 44 (Answer) / 53
Try this!5) Construct an equilateral triangle that has a side length of 6.7 cm using a protractor and a ruler.
Video: Constructing Equilateral Triangles
[This object is a pull tab]
Ans
wer
Circulate around the room to make sure that the students are constructing the triangles correctly. Diagrams should resemble the figure below.
6.7 cm
6.7 cm6.7 cm
![Page 67: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/67.jpg)
Slide 45 / 53
Example Use a ruler & a protractor to draw ∆ FGH that satisfies the following conditions. 1. m∠F = 30° 2. m∠G = 70° 3. FG = 8 cm
Step #1: Reread your question. We know two angle measurements and the length of 1 side. Let's start with the side, since at least 1 segment is required to use a protractor.
Step #2: Draw your 8 cm segment. Label one endpoint with F & the other with G
F G
![Page 68: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/68.jpg)
Slide 46 / 53
F G
Step #2: With your protractor, place its center at point F. Measure the 30° required for m ∠F. Draw a line through the 30° angle
F G
Step #3: With your protractor, place its center at point G. Measure the 70° required for m ∠G. Draw a line through the 70° angle
![Page 69: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/69.jpg)
Slide 47 / 53
Step #4: Draw point H where the 2 lines intersect & erase any additional lines.
F G
H
30° 70°8 cm
![Page 70: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/70.jpg)
Slide 48 / 53
Try this!6) Construct ∆JKL with the given conditions using a protractor and a ruler. 1. m∠K = 105° 2. m∠L = 25° 3. KL = 9 cm
Video: Constructing Triangles
![Page 71: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/71.jpg)
Slide 48 (Answer) / 53
Try this!6) Construct ∆JKL with the given conditions using a protractor and a ruler. 1. m∠K = 105° 2. m∠L = 25° 3. KL = 9 cm
Video: Constructing Triangles
[This object is a pull tab]
Ans
wer
Circulate around the room to make sure that the students are constructing the triangles correctly. Their diagrams should resemble the figure below.
L K
J
9 cm105°25°
![Page 73: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/73.jpg)
Slide 49 (Answer) / 53
Glossary
Return toTable ofContents
[This object is a pull tab]
Teac
her N
otes Vocabulary Words are bolded
in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
![Page 74: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/74.jpg)
Slide 50 / 53
Back to
Instruction
Compass
An instrument with 2 arms, one sharp & one with a pencil that can be used to
draw circles and arcs.
![Page 75: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/75.jpg)
Slide 51 / 53
Back to
Instruction
Protractor
An instrument used to measure angles. They are usually half of a circle (180°). To measure an angle, line up the protractor so that the vertex of the angle aligns with the small hole, or dot, near the bottom of the protractor and one of the angle
edges lies on the straight line at the bottom.
30°
90°
135°
![Page 76: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/76.jpg)
Slide 52 / 53
Back to
Instruction
Ruler
An instrument used to measure the lengths of segments.
A
B
C
D
E
F
AB = 3.5 cm
CD = 5 cm
EF = 6.5 cm
![Page 77: Slide 1 / 53content.njctl.org/courses/math/7th-grade/drawing-geometric-figures/... · Slide 9 / 53 Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test](https://reader034.vdocument.in/reader034/viewer/2022050120/5f509915c0f0023a531709b4/html5/thumbnails/77.jpg)
Slide 53 / 53
Back to
Instruction
5
103
510
3
5 + 3 > 10
Triangle Inequality
The sum of the lengths of any two sides of a triangle is greater than the length
of the third side.
6
104
610
4
6 + 4 > 10
7
105
7
10
5
7 + 5 > 10