Page 120 - Math Course 3 (Book 2)

Similarity of Polygons

Since both triangles are isosceles, the base angles The ratios of the measures of the corresponding

in each triangle are congruent. In the first triangle, sides are equal.
180 – 40
the base angles measure or 700 and in
2 The ratio of the measures of the
the second triangle, the base angles measure Answer corresponding sides are equal
180 – 50
or 650 and the corresponding angles are
2 congruent, so ΔABC ~ ΔRST.

None of the corresponding angles
Answer are congruent, so the triangles are
not similar Real World Example

ARCHITECTURE
Determine whether each pair of figures is similar. An architect prepared a 12-inch model
Justify your answer of a skyscraper to look like a real
1100-foot building. What is the scale
factor of the model compared to
the real building?
B

Before finding the scale factor
800 7 you must make sure that both
measurements use the same
5.2 unit of measure.

600 1 foot = 12 inches

A 8 C
1 foot = 12 inches
S 1100 feet 13,200 inches

800 1
5.25 = 1100
3.9
400 The ratio comparing the two
1
heights is or 1:1100. The
R 6 T 1100
1
Answer scale factor is , which means
1100
∠B ≅ ∠S; m∠C = 40 by the Angle Sum Theorem; that the model is the height of
1
m∠R = 60 by the Angle Sum Theorem; therefore 1100
∠C ≅ ∠T and ∠A ≅ ∠R. the real skyscraper.
All the corresponding angles are congruent.

Now determine whether corresponding sides are
proportional.

AC 8
= or 1.3
RT 6

BC 7
= or 1.3
ST 5.25

AB 5.2
= or 1.3
RS 3.9

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