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Geometry 7.4 AA Similarity Postulate

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An Experiment Draw any two segments AB and CD. Draw any angle at A and a congruent angle at C. Draw any angle at B and a congruent angle at D. BACD The third angle is also congruent Corresponding sides are proportional. Thus, the triangles are similar.

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AA Similarity Postulate If two angles of one triangle are congruent to two angles another triangle, then the triangles are similar. ~

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50 60 50 70 45 I. Are these triangles similar? (yes, no, no conclusion) 1. Answer: ______ 2. Answer: ______ 3. Answer: ______ 4. Answer: ______ 5. Answer: ______ 6. Answer: ______ 62 60 54 60 40 75

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2 4 y x 3 6 y 4 5 x 6 8 8 10 y 12 x 5 8 x y 10.5 7 4 II. Find x,y using proportions if possible. 7. x= ______ y= ______ 8. x= ______ y= ______ 9. x= ______ y= ______ 10. x= ______ y= ______

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6 15 10 x 12 y x y 5 10 6 9 11. x= ______ y= ______ 12. x= ______ y= ______

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Given: Prove: Given: Prove: A B C D E 1 2 X F S R E

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HW P. 257-259 1-17, 20, 21b, 23 -A note about the HW Questions we do on the board the next day.

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Are the triangles similar? Yes, no, or no conclusion. 60 54 62 o o o o 66 o 58 o No, the triangles only have one congruent angle.

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Are the triangles similar? Yes, no, or no conclusion. 60 70 50 o o o o 70 o 60 o Yes, the triangles are similar by AA ~ Post.

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Are the triangles similar? Yes, no, or no conclusion. Yes, the triangles are similar by AA ~ Post.

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Are the triangles similar? Yes, no, or no conclusion. Thus, the triangles are not necessarily similar, but they may be similar. Therefore, no conclusion. One angle is congruent, and the other angles may or may not be congruent.

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Are the triangles similar? Yes, no, or no conclusion. 75 40 o o 70 o 30 o No, the triangles have no congruent angles. 75 o 70 o

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Are the triangles similar? If yes, find x and y using proportions. 19 15 5 x 12 y 20 3 4 The triangles are similar by The AA ~ Post. 3 3 x = 9 3y = 76 y = 25 and 1/3

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Are the triangles similar? If yes, find x and y using proportions. 10.5 7 4 x 8 y Yes, the triangles are similar by AA ~ Post. The figures are not drawn to scale. The scale factor is 7:4. 7 4 7x = 42 x = 6 2 2 y = 14

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A Few Together from the HW P. 258 #20 P. 259 #23

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Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.

Solve the following proportions. a = 9 b = 7 c = 6 d = ±6.

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