Download 7.4 AA Similarity Postulate

Geometry
7.4 AA Similarity Postulate
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
AA Similarity Postulate
 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, no conclusion)
1.
2.
Answer: ______
Answer: ______
3.
4.
Answer: ______
Answer: ______
5.
40
70
60
60
60
50
50
54
62
75
6.
45
Answer: ______
Answer: ______
45
II. Find x,y using proportions if possible.
7.
8.
x
y
4
5
8
4
x
y
6
3
2
6
x= ______
x= ______
y= ______
y= ______
9.
10.
10
y
8
10.5
5
7
12
y
x
4
x
8
x= ______
x= ______
y= ______
y= ______
11.
12.
5
x
y
x
12
10
15
y
10
6
9
6
x= ______
x= ______
y= ______
y= ______
Given: 1  2
C
F
D
Prove: BD  CA  BC  DE
A
S
Given: EF // RS
1
2
E
Prove: FX EF

SX
RS
B
X
E
R
HW
P. 257-259 1-17, 20, 21b, 23
-A note about the HW Questions we do on the board the next day.
Are the triangles similar?
Yes, no, or no conclusion.
54o
o
62
o
60
o
60
58o
66o
No, the triangles only have one congruent angle.
Are the triangles similar?
Yes, no, or no conclusion.
50
o
o
50
o
60
70o
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 by AA ~ Post.
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.
40o
75o
o
75
70o
30o
70o
No, the triangles have no congruent angles.
Are the triangles similar? If yes,
find x and y using proportions.
The triangles are similar by
The AA ~ Post.
12
y
Scale factor
15 3

20 4
3 3 x

4 3 12
4
x
19
x=9
5
15
3 19

4 y
20
3y = 76
y = 25 and 1/3
3
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.
10.5
7
7
7 10.5

4
x
7x = 42
4
4
8
x
x=6
72 y

42 8
y = 14
A Few Together from the HW
P. 258 #20
P. 259 #23