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# At a Glance - Similar Figures

Similar figures have the same shape, but might not be the same size

• When two shapes are similar, their corresponding sides are proportional (see ratios and proportions) and their corresponding angles are congruent.
• An older sister and a younger sister might be considered similar

Congruent figures have the same shape and size.

• When two shapes are congruent, their corresponding sides and angles are congruent.
• Identical twins might be considered congruent

Here are two symbols that you need to know:

~ means similar
≅ means congruent

Look Out: be careful when reading which sides correspond to each other; the shapes may be rotated.

#### Example 1

 Quadrilaterals ABCD and EFGH are congruent (ABCD ≅ EFGH). Find the measure of each missing angle and side.

#### Example 2

 Triangles ABC and DEF are similar (ABC ~ DEF). What is the length of side DF?

#### Example 3

 The sun casts a shadow on two trees in a field. The smaller of the two is 10.5 ft high and has a shadow 11.25 ft long. The shadow of the taller tree is 17.5 ft long. How tall is that tree?This is actually how the heights of many tall structures are estimated!

#### Example 4

 Pentagons OPQRS and TUVWX are both regular. Find the length of the apothem of TUVWX. The apothem is the distance from the center of a regular polygon to the midpoint of one side.

#### Exercise 1

What are m &ang; K and m of line MJ?

#### Exercise 2

Triangle RST ~ Triangle UVW. Find the length of sides ST and VU. Round to the nearest hundredths place.

#### Exercise 3

The sun casts a 23 foot shadow on a flagpole. You are 5 feet 3 inches and cast an 11 foot shadow. Approximately how tall is the flagpole? Round to the nearest hundredths place.

#### Exercise 4

One square has side lengths of 5 cm, and a diagonal ≅ 7.07 cm. Another square has side lengths of 8 cm. What is the length of its diagonal?