Geometry 7 4 AA Similarity Postulate An Experiment

  • Slides: 16
Download presentation
Geometry 7. 4 AA Similarity Postulate

Geometry 7. 4 AA Similarity Postulate

An Experiment l Draw any two segments AB and CD. l Draw any angle

An Experiment l Draw any two segments AB and CD. l Draw any angle at A and a congruent angle at C. l 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

AA Similarity Postulate l If two angles of one triangle are congruent to two

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

I. Are these triangles similar? (yes, no conclusion) 1. 2. 54 62 Answer: ______

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

II. Find x, y using proportions if possible. 7. 8. x y 4 5

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

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

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

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

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

HW P. 257 -259 1 -17, 20, 21 b, 23 -A note about the

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

Are the triangles similar? Yes, no, or no conclusion. 54 o o 62 o

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

Are the triangles similar? Yes, no, or no conclusion. o o 50 50 o

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

Are the triangles similar? Yes, no, or no conclusion. Yes, the triangles are similar

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

Are the triangles similar? Yes, no, or no conclusion. One angle is congruent, and

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.

Are the triangles similar? Yes, no, or no conclusion. 40 o 75 o o

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

Are the triangles similar? If yes, find x and y using proportions. The triangles

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

Are the triangles similar? If yes, find x and y using proportions. Yes, the

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 10. 5 4 4 8 7 The scale factor is 7: 4. 7 x 7 x = 42 x=6 2 2 y = 14

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

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