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Geometry

Explore the concept of AA Similarity Postulate through an experiment with drawing segments, angles, and triangles. Determine triangle similarity using corresponding angle measurements. Utilize proportions to find unknown values.

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Geometry

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  1. Geometry 7.4 AA Similarity Postulate

  2. 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. The third angle is also congruent Corresponding sides are proportional. Thus, the triangles are similar. A B C D

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

  4. 54 50 62 50 60 70 60 60 75 40 45 45

  5. y 5 4 x x 8 4 6 3 y 2 6 10 8 5 y 12 y 10.5 7 x x 4 8

  6. 5 x 15 6 x y y 10 12 10 6 9

  7. S C F D 1 2 R A X B E E

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

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

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

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

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

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

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

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

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

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