6.2 – use proportions to solve geometry problems
DESCRIPTION
6.2 – Use Proportions to Solve Geometry Problems. Complete the statement. y. If. , then. x. Complete the statement. x. If. , then. y. Complete the statement. 9+ y. If. , then. y. Complete the statement. 5+11. If. , then. 11. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/1.jpg)
6.2 – Use Proportions to Solve Geometry Problems
![Page 2: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/2.jpg)
Property Result
Reciprocal Property
Interchange Means
Adding
,a c
If thenb d
=
,a c
If thenb d
=
a b c d
b d
+ +=
b d
a c=
a b
c d=
,a c
If thenb d
=
![Page 3: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/3.jpg)
Complete the statement.
y
x=
107
?
?
7
10=If , then
y
x
![Page 4: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/4.jpg)
?
?
24
6=If , then
x
y
Complete the statement.
yx
246=
![Page 5: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/5.jpg)
?
?3=
+xxIf , then 9+y
y
Complete the statement.
yx
93=
![Page 6: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/6.jpg)
?
?=
+yyx
If , then 5+1111
Complete the statement.
11
5=
yx
![Page 7: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/7.jpg)
Use the given information and the diagram to find the unknown length.
1
x=
3x = 2
x =23
3
2
![Page 8: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/8.jpg)
Use the given information and the diagram to find the unknown length.
3
4=
3x = 24
x = 8
6
x
![Page 9: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/9.jpg)
Use the given information and the diagram to find the unknown length.
12
x=
18x = 180
x = 10
18
15
![Page 10: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/10.jpg)
Use the given information and the diagram to find the unknown length.
12
9=
12x = 144
x = 12
16
x
![Page 11: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/11.jpg)
6.3 – Use Similar Polygons
![Page 12: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/12.jpg)
Similar Polygons:
• Corresponding angles are congruent
• Corresponding sides are proportional
![Page 13: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/13.jpg)
Scale Factor:
The ratio of the lengths of two corresponding sides of similar figures.
![Page 14: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/14.jpg)
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.
=DE
AB
Angles
A D
B E
C F
Sides: =EF
BCDF
AC
![Page 15: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/15.jpg)
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality.
=MJ
CD
Angles
C M
D J
E K
Sides: =JK
DE
ML
CF
F L
=KL
EF
![Page 16: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/16.jpg)
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor.
Angles
A F
B D
C E
Sides: =6
3
2
1
=10
5
2
1
=8
4
2
1
![Page 17: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/17.jpg)
Yes, they are similar.
ABC ~
Scale factor:2
1
FDE
![Page 18: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/18.jpg)
Angles
Q W
R X
S YT Z
Sides: =3
6
1
2
=6
8
3
4
No, they are not similar.
![Page 19: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/19.jpg)
The polygons are similar as noted. Find the value of x.
6
4=
6x = 48
x = 8
12
x
![Page 20: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/20.jpg)
The polygons are similar as noted. Find the value of x.
8
12=
8x = 144
x = 18
BCED ~ KLMJ12
x
![Page 21: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/21.jpg)
The two triangles are similar. Find the values of the variables.
6
12=
6m = 66
m = 11
6
12=
12n = 48
n = 4
5.5
m 8
n
![Page 22: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/22.jpg)
5. The two figures are similar. Find the scale factor of their sides. Then find the ratios of their perimeters. What do you notice?
18
6 4
12128
Scale Factor:12
8=
3
2
Ratio of Perimeters:36
24=
3
2
They are the same!
![Page 23: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/23.jpg)
Ratios of Perimeters:
If two polygons are similar, then the ______ of their __________ is equal to the ratios of their corresponding ____ lengths
ratioperimeters
side
![Page 24: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/24.jpg)
The ratio of one side of a picture to the corresponding side of a larger picture is 2:7. The perimeter of the smaller picture is 16 inches. Find the perimeter of the larger picture.
2
7=
2x = 112
x = 56in
2
7
16x
16
x
![Page 25: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/25.jpg)
In the diagram, MNOP ~ WXYZ .
a.Find the scale factor of MNOP to WXYZ .
5
4
10
8=
![Page 26: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/26.jpg)
In the diagram, MNOP ~ WXYZ .
b. Find the values of x, y, and z.
5
4=
4x = 60
x = 15
5
4=
5y = 40
y = 8
z° = 135°12
x 10
y
![Page 27: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/27.jpg)
In the diagram, MNOP ~ WXYZ .
c. Find the perimeter of MNOP.
10 + 15 + 10 + 15
50
![Page 28: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/28.jpg)
d. Find the ratio of the perimeter of MNOP to the perimeter of WXYZ.
In the diagram, MNOP ~ WXYZ .
12 + 8 + 12 + 8
40
PerimeterMNOP
PerimeterWXYZ=
5
4
50
40=
![Page 29: 6.2 – Use Proportions to Solve Geometry Problems](https://reader036.vdocument.in/reader036/viewer/2022062518/56814a9d550346895db7ad2b/html5/thumbnails/29.jpg)
HW Problem
6.3 # 12
Ans:
6.2
6.3
367-369
376-378
3-11 odd, 12, 16-18, 28, 29
3, 7-12, 19, 20, 31, 32
36in5
3=
60x