6.2 – use proportions to solve geometry problems
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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
6.2 – Use Proportions to Solve Geometry Problems
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
Complete the statement.
y
x
10
7
?
?
7
10If , then
y
x
?
?
24
6If , then
x
y
Complete the statement.
yx
246
?
?3
x
xIf , then 9+yy
Complete the statement.
yx
93
?
?
y
yxIf , then 5+11
11
Complete the statement.
11
5
y
x
Use the given information and the diagram to find the unknown length.
1
x
3x = 2
x =23
3
2
Use the given information and the diagram to find the unknown length.
3
4
3x = 24
x = 8
6
x
Use the given information and the diagram to find the unknown length.
12
x
18x = 180
x = 10
18
15
Use the given information and the diagram to find the unknown length.
12
9
12x = 144
x = 12
16
x
6.3 – Use Similar Polygons
Similar Polygons:
• Corresponding angles are congruent
• Corresponding sides are proportional
Scale Factor:
The ratio of the lengths of two corresponding sides of similar figures.
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
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
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
Yes, they are similar.
ABC ~
Scale factor:2
1
FDE
Angles
Q W
R X
S YT Z
Sides: 3
6
1
2
6
8
3
4
No, they are not similar.
The polygons are similar as noted. Find the value of x.
6
4
6x = 48
x = 8
12
x
The polygons are similar as noted. Find the value of x.
8
12
8x = 144
x = 18
BCED ~ KLMJ12
x
The two triangles are similar. Find the values of the variables.
5.5
m
6m = 66
m = 11
6
12 8
n
The two triangles are similar. Find the values of the variables.
5.5
m
6m = 66
m = 1112n = 48
n = 4
6
12 8
n
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!
Ratios of Perimeters:
If two polygons are similar, then the ______ of their __________ is equal to the ratios of their corresponding ____ lengths
ratioperimeters
side
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
7. In the diagram, WXYZ ~ BCDE.
a.Find the scale factor of WXYZ to BCDE.
6
4
3
2
7. In the diagram, WXYZ ~ BCDE.
b. Find the values of XY and YZ.
3
2
3
XY
6
YZ
2XY = 9
XY = 4.5
4.5 4.5
7. In the diagram, WXYZ ~ BCDE.
b. Find the values of XY and YZ.
3
2
3
XY
6
YZ
2YZ = 18
YZ = 9
2XY = 9
XY = 4.5
4.5 4.5
9
7. In the diagram, WXYZ ~ BCDE.
c. Find mC.
mC = 117°
4.5 4.5
9
d. Find the perimeter of WXYZ.
7. In the diagram, WXYZ ~ BCDE.
4.5 4.5
99 + 4.5 + 4.5 + 6
24u
HW Problem
6.3 # 12
6.2
6.3
367-369
376-378
11, 12, 16, 17, 28, 29
3, 7-12, 19, 20
x = 36in
5
3
60
x
35
x60