ABC ~ XYZ
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GEOMETRY HELP ABC ~ XYZ Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. Complete each statement. a. mB = ? b. BC YZ = ? XZ a. B Y and mY = 78, so mB = 78 because congruent angles have the same measure. b. Because AC corresponds to XZ, . = BC YZ AC XZ Quick Check Similar Polygons LESSON 7-2 Additional Examples
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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. - PowerPoint PPT Presentation
Transcript of ABC ~ XYZ
GEOMETRYHELP
ABC ~ XYZ
Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional.
Complete each statement. a. mB = ?
b. BCYZ
= ? XZ
a. B Y and mY = 78, so mB = 78 because congruent angles have the same measure.
b. Because AC corresponds to XZ, .=BCYZ
ACXZ
Quick Check
Similar PolygonsLESSON 7-2
Additional Examples
GEOMETRYHELP
Determine whether the parallelograms are similar. Explain.
Corresponding sides of the two parallelograms are proportional.
Although corresponding sides are proportional, the parallelograms are not similar because the corresponding angles are not congruent.
Check that corresponding angles are congruent.
B corresponds to K, but mB ≠ mK, so corresponding angles are not congruent.
Check that the corresponding sides are proportional.
= = = =ABJK
24
BCKL
12
CDLM
24
DAMJ
12
Similar PolygonsLESSON 7-2
Additional Examples
Quick Check
GEOMETRYHELP
If ABC ~ YXZ, find the value of x.
Because ABC ~ YXZ, you can write and solve a proportion.
x = 401230
Solve for x.
x = 16
= Corresponding sides are proportional.ACYZ
BCXZ
= Substitute. x 40
1230
Similar PolygonsLESSON 7-2
Additional Examples
Quick Check
GEOMETRYHELP
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.
Similar PolygonsLESSON 7-2
Additional Examples
Quick Check
postcard width postcard lengthpainting width painting length= Corresponding sides are proportional.
= Substitute. x 24
6 36
6 36x = 24 Solve for x.
GEOMETRYHELP
The dimensions of a rectangular tabletop are in the golden
ratio. The shorter side is 40 in. Find the longer side.
Let represent the longer side of the tabletop.
= 64.72 Cross-Product Property
The table is about 65 in. long.
Similar PolygonsLESSON 7-2
Additional Examples
Quick Check
40
= Write a proportion using the golden ratio. 1.618 1
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