4.2
DESCRIPTION
4.2. How Can I Use Equivalent Ratios? Pg. 7 Applications and Notation. 4.2– How Can I Use Equivalent Ratios? Applications and Notation. Now that you have a good understanding of how to determine similarity, you are going to use proportions to find missing parts of similar shapes. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/1.jpg)
4.2
How Can I Use Equivalent Ratios?Pg. 7
Applications and Notation
![Page 2: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/2.jpg)
4.2–How Can I Use Equivalent Ratios?Applications and Notation
Now that you have a good understanding of how to determine similarity, you are going to use proportions to find missing parts of similar shapes.
![Page 3: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/3.jpg)
4.12 – EQUAL RATIOS OF SIMILARITYCasey wants to enlarge a letter "C". a. Since the zoom factor multiplies each side of the original shape, then the ratio of the widths must equal the ratio of the lengths. Casey decided to show these ratios in the diagram at right. Verify that her ratios are equal by reducing each one.
![Page 4: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/4.jpg)
248
186
31
31
![Page 5: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/5.jpg)
86
4=3
2418
4=3
![Page 6: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/6.jpg)
c. She decided to create an enlarged "C" for the door of her bedroom. To fit, it needs to be 20 units tall. If x is the width of this "C", write and solve an proportion to find out how wide the "C" on Casey's door must be. Be ready to share your equation and solution with the class.
![Page 7: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/7.jpg)
8=6820
=
8x = 120x = 15
8x = 120x = 15
20x
6x
![Page 8: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/8.jpg)
4.13 – PROPORTIONSUse your observations about ratios between similar figures to answer the following: a. Are the triangles similar? How do you know?
6=321
10=521
74
Not similar
![Page 9: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/9.jpg)
b. If the pentagons at right are similar, what are the values of x and y?
8 =2424y = 144
y = 6
y18
8 =248x = 264x = 33
11x
![Page 10: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/10.jpg)
Proportion
How to Solve
1._____________________________________
2. ____________________________________
3. ____________________________________
ab
cd
Reduce around the boxCross multiply
Solve
![Page 11: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/11.jpg)
4.14 – SOLVING PROPORTIONS
![Page 12: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/12.jpg)
1 3
x 9=
![Page 13: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/13.jpg)
y 9=
![Page 14: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/14.jpg)
1
5
x + 2 5=x 3=
![Page 15: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/15.jpg)
1 2
2x x + 8= x 8=
![Page 16: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/16.jpg)
13
3(x – 12) x=3x – 36 x=2x – 36 0=
2x 36=x 18=
![Page 17: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/17.jpg)
1 2
2(y + 1) y + 4=2y + 2 y + 4=
y + 2 4=y 2=
![Page 18: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/18.jpg)
4.15 – PROPORTIONS You used a proportion equation to solve the previous problem. It is important that parts be labeled to help you follow your work. The same measures need to match to make sure you will get the right answer. Likewise, when working with geometric shapes such as the similar triangles below, it is easier to explain which sides you are comparing by using notation that everyone understands.
![Page 19: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/19.jpg)
ACCB =
ABBC =
ABDE =
DFFE
DEEF
ACDF
![Page 20: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/20.jpg)
Yes, angles need to add to 180°
![Page 21: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/21.jpg)
![Page 22: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/22.jpg)
a. What other angles should match up?
B XC Y
![Page 23: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/23.jpg)
b. Complete the similarity statement for the triangles.
ABC ~ ___________ZXY
![Page 24: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/24.jpg)
4.17 – READING SIMILARITY STATEMENTS Read the similarity statements below. Determine which angles must be equal. Then determine which sides match up.
![Page 25: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/25.jpg)
D
E
F
DEEFDF
![Page 26: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/26.jpg)
F
U
N
FUUNFN
![Page 27: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/27.jpg)
4.18 – READING SIMILARITY STATEMENTS Examine the triangles below. Which of the following statements are correctly written and which are not? Hint: two statement is correct.
![Page 28: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/28.jpg)
4.19 – PROPORTION PRACTICE Find the value of the variable in each pair of similar figures below. Make sure you match the correct sides together.
![Page 29: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/29.jpg)
![Page 30: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/30.jpg)
a. ABCD ~ JKLM
69=
12x21
x 18=
![Page 31: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/31.jpg)
NOP ~ XYZ
w5=
12341
w 20=
![Page 32: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/32.jpg)
GHI ~ PQR
3n
= 7
167n = 48
n = 6.86
![Page 33: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/33.jpg)
ABC ~ XYZ
7m
= 1011
10m = 77m = 7.7
![Page 34: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/34.jpg)
23
12x
1 4
x 8=
![Page 35: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/35.jpg)
74
21
2 4x
1 3
2x + 4 12=2x 8=x 4=
![Page 36: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/36.jpg)
4.20 – NESTING TRIANGLES Rhonda was given the diagram and told that the two triangles are similar. a. Rhonda knows that to be similar, all corresponding angles must be equal. Are all three sets of angles equal? How can you tell?
AEB ADC ABE ACD
A A
![Page 37: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/37.jpg)
b. Rhonda decides to redraw the shape as two separate triangles, as shown. Write a proportional equation using the corresponding sides, and solve. How long is AB? How long is AC?
xx 8
4x + 32 = 11x 32 = 7x
4.57 = x
44 7
![Page 38: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/38.jpg)
![Page 39: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/39.jpg)
Get out your cartoon
![Page 40: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/40.jpg)
Put graph paper over the cartoon and trace
![Page 41: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/41.jpg)
Draw a box around the graph
![Page 42: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/42.jpg)
Count the base and height of box
![Page 43: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/43.jpg)
Get large graph paper for group
![Page 44: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/44.jpg)
Draw the same size box on big grid
![Page 45: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/45.jpg)
Divide up evenly within the group
![Page 46: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/46.jpg)
Cut both pieces of graph paper
![Page 47: 4.2](https://reader035.vdocument.in/reader035/viewer/2022070421/5681616c550346895dd0fa0a/html5/thumbnails/47.jpg)