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Similar figures

# Similar figures: side lengths and angle measures

Two polygons are similar if these two facts both must be true:

• Corresponding angles are equal.
• The ratios of pairs of corresponding sides must be equal.
(in other words, if they are proportional).
The symbol for "is similar to" is $\sim$

If these two shapes are similar, what is the measure of the missing length b?

The corresponding sides of similar shapes are proportional.

The trapezoids' longer sides have a ratio of $\frac{6}{28}$, which is $\frac{3}{14}$.

The trapezoids' shorter sides have a ratio of $\frac{b}{14}$.

Write a proportion:

$\frac{3}{14}=\frac{b}{14}$

Find the cross products and solve:

 42 = 14b 42 ÷ 14 = 14b ÷ 14 3 = b

The missing length is 3 kilometers.

If these two shapes are similar, what is the measure of the missing length z?

 105 yd 21 yd z 50 yd

z = yd