Transcript Similar Polygons LESSON 7-2 Additional Examples ABC ~ XYZ Complete each statement. a. mB = ? b.

Similar Polygons
LESSON 7-2
Additional Examples
ABC ~
XYZ
Complete each statement.
a. mB = ?
b. BC = ?
YZ
XZ
Two polygons are similar if (1) corresponding angles are congruent
and (2) corresponding sides are proportional.
a. B Y and mY = 78, so mB = 78 because congruent angles
have the same measure.
b. Because AC corresponds to XZ, BC = AC.
YZ
XZ
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HELP
GEOMETRY
Similar Polygons
LESSON 7-2
Additional Examples
Determine whether the parallelograms are similar. Explain.
Check that the corresponding sides are proportional.
AB 2
=
JK 4
BC 1
=
KL
2
CD 2
=
LM 4
DA 1
=
MJ 2
Corresponding sides of the two parallelograms are
proportional.
Check that corresponding angles are congruent.
B corresponds to K, but mB ≠ mK, so corresponding angles are not
congruent.
Although corresponding sides are proportional, the parallelograms are not
similar because the corresponding angles are not congruent.
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HELP
GEOMETRY
Similar Polygons
LESSON 7-2
Additional Examples
If
Because
ABC ~
ABC ~
YXZ, find the value of x.
YXZ, you can write and solve a proportion.
AC BC
=
YZ XZ
Corresponding sides are proportional.
x = 12
40
30
Substitute.
x = 12  40
Solve for x.
30
x = 16
Quick Check
HELP
GEOMETRY
Similar Polygons
LESSON 7-2
Additional Examples
A painting is 24 in. wide by 36 in. long. The length of a
postcard reduction of the painting is 6 in. How wide is the postcard?
The postcard and the painting are similar rectangles, so you can write a
proportion. Let x represent the width of the postcard.
postcard width
postcard length
=
painting width
painting length
x
6
=
24
36
6
x = 36  24
Corresponding sides are proportional.
Substitute.
Solve for x.
x=4
The postcard is 4 in. wide.
HELP
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GEOMETRY
Similar Polygons
LESSON 7-2
Additional Examples
The dimensions of a rectangular tabletop are in the golden
ratio. The shorter side is 40 in. Find the longer side.
Let
40
represent the longer side of the tabletop.
= 1.618
Write a proportion using the golden ratio.
= 64.72
Cross-Product Property
1
The table is about 65 in. long.
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HELP
GEOMETRY