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ABC ~ XYZ PowerPoint PPT Presentation


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BC YZ. ? XZ. =. a.  B  Y and m  Y = 78, so m  B = 78 because congruent angles have the same measure. AC XZ. BC YZ. b. Because AC corresponds to XZ ,. =. Similar Polygons. LESSON 7-2. Additional Examples. ABC ~ XYZ. Complete each statement. a. m  B = ? b.

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ABC ~ XYZ

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Abc xyz

BC

YZ

?

XZ

=

a.BY and mY = 78, so mB = 78 because congruent angles have the same measure.

AC

XZ

BC

YZ

b.Because AC corresponds to XZ, .

=

Similar Polygons

LESSON 7-2

Additional Examples

ABC ~ XYZ

Complete each statement.

a.mB = ?

b.

Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional.

Quick Check


Abc xyz

Check that the corresponding sides are proportional.

1

2

AB

JK

2

4

BC

KL

1

2

CD

LM

2

4

DA

MJ

=

=

=

=

Similar Polygons

LESSON 7-2

Additional Examples

Determine whether the parallelograms are similar. Explain.

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.

Quick Check


Abc xyz

Because ABC ~ YXZ, you can write and solve a proportion.

AC

YZ

BC

XZ

=

Corresponding sides are proportional.

x

40

12

30

=

Substitute.

12

30

Solve for x.

x =  40

Similar Polygons

LESSON 7-2

Additional Examples

If ABC ~ YXZ, find the value of x.

x = 16

Quick Check


Abc xyz

postcard widthpostcard length

painting widthpainting length

Corresponding sides are proportional.

=

x

24

6

36

=

Substitute.

6

36

Solve for x.

x =  24

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.

x = 4

The postcard is 4 in. wide.

Quick Check


Abc xyz

Let represent the longer side of the tabletop.

40

1.618

1

Write a proportion using the golden ratio.

=

= 64.72

Cross-Product Property

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.

The table is about 65 in. long.

Quick Check


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