Page 122 - Math Course 3 (Book 2)

Similarity of Polygons

MO. 10 - L2b Use the congruent angles to write the
corresponding vertices in order.
Solving Problems Involving polygon ABCDE ~ polygon RSTUV

Scale Factor
Now write proportions to find x and y.

To find x:
Vocabulary A-Z

Let us learn some vocabulary AB CD Similarity proportion

RS = TU
scale factor 6 = X AB = 6, RS = 4, CD = x, TU =3
The ratio of any two corresponding lengths in two 4 3
similar geometric figures is called the scale factor.
6(3) = 4x Cross products
B E

18 = 4x Multiply.
15 18 5 6
9 = X Divide each side by 4.
2

To find y:
A 9 C D 3 F

The scale factor, or AB = BC = AC AB = DE Similarity proportion
similarity ratio, of △ABC DE EF DF RS UV
to △DEF is 3 15 18 9 3 6 = 8 AB = 6, RS = 4, DE = 8, UV = y + 1
1 = = = 4 y + 1
5 6 3 1
6(y + 1) = 4(8) Cross products

Let’s Begin 6y + 6 = 32 Multiply.

6y = 26 Subtract 6 from each side.
Proportional Parts and Scale Factor

Example y = 13 Divide each side by 6 and
simplify.
3
13 16
UV = y + 1, so UV = + 1 or
3 3
The two polygons are similar. Write a similarity
statement. Then find x, y, and UV. ABCDE ~ RSTUV;
6 B Answer x = 9 ; y = 13 ; UV = 16
2 3 3
A C

x
4 S
E 8 D R T
3

V y + 1 U
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