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In this unit, we explore the Angle-Angle (AA) Similarity Theorem, which states that if two triangles have two pairs of congruent angles, the third pair is also congruent, ensuring the triangles are similar. We will engage in problem-solving exercises involving identifying similar triangles, determining angle measures, and using proportional sides to establish similarity. Through interactive activities and practice problems, students will solidify their understanding of triangle similarity, crucial for further applications in geometry and real-world scenarios.
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Similar Triangles Unit 4.16
AA (Angle Angle) Similarity Theorem N If two triangles have two pairs of congruent angles, then the third pair of angles is also congruent and the triangles are Similar. H 35° 35° M G K P Triangle GHK is similar to triangle MNP:
Let’s Try It! 1) 2) x + 28 + 80 = 180 X + 108 = 180 X = 72 28 + 71 + y = 180 Y + 99= 180 66 + 90 + x = 180 x + 156= 180 y = 81 x = 24 NOT Similar! Similar! (We only need 2 congruent pairs)
3) 42° 90° 48°
You Try It! 4) 5)
You Try It! 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.
You Try It! 8)
You Try It! 9) The flagpole is 35 ft. tall!
You Try It! 10)
Homework Time Simply Similar! WS
