Similar TrianglesUnit 4.16

AA (Angle Angle) Similarity Theorem

If two triangles have two pairs of congruent angles, then the third pair of angles is also congruent and the triangles are Similar.

35°

35°

G

H

K

N

M P

Triangle GHK is similar to triangle MNP:

c.

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1) 2)

x + 28 + 80 = 180

X + 108 = 180

X = 72

28 + 71 + y = 180

Y + 99 = 180

y = 81

NOT Similar!

66 + 90 + x = 180

x + 156 = 180

x = 24

Similar!

(We only need 2 congruent pairs)

3) 42°

90°

48°

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4)

5)

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6) 7)

Proportional Sides of Similar Triangles

Two triangles are similar if and only if the proportions of their corresponding side lengths are equal.

is similar to because the proportions of their corresponding side lengths are equal.

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8)

9)

The flagpole is 35 ft. tall!

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10)

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Homework Time

Simply Similar! WS