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Lesson 7-3
D
Objective – To prove triangles similar using
AA, SSS, and SAS.
AA Postulate
If two angles of one triangle are congruent to two
angles of another, then the triangles are similar.
Z
B
A
C
X
Y
B
Given: BC  DE
Prove: ABC ADE
A
Statement
C
E
Reasons
1) BC  DE
Given
2) BCA  DEA
Corres. s Postulate
3) A  A
Reflexive Prop. of 
4) ABC ADE
AA Simlarity
ABC  X ZY
SSS Similarity
If three sides of one triangle are proportional to
three corresponding sides of another triangle, then
the triangles are similar.
E
B
9
9
A
C
12
AB  9  3
ED 12 4
BC  9  3
DF 12 4
AC  12  3
EF 16 4
D
F
12
12
M  P by Alternate Interior s Thm.
 MN = LN  10 = x
PN NO
12 15
 ABC  E D F
150  12x
E
B
C
D
15
AB  6  2
DE 9 3
 ABC  DEF
F
x  12.5
Explain how to find x.
B
8
A
9
AC  10  2
DF 15 3
N
 MNL PNO by AA Similarity.
6
10
x
L
O
15
10
MNL  PNO by Reflexive Prop of  .
SAS Similarity
If two sides of one triangle are proportional to two
sides of another triangle and the included angles
are congruent, then the triangles are congruent.
A
M
P
16
12
Explain how to find x.
D
4
6
12
C 6
x
E
It is given in the drawing, AB  8  2 , and
AD 12 3
AB
AC
by substitution.


AD AE

A  A by Reflexive Prop of  .
 ABC ADE by SAS Similarity.
A  D
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
AC  12  2 .
AE 18 3
12  6
18 x
12x  108
x 9
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Lesson 7-3
If each pair of triangles is similar, explain why.
If each pair of triangles is similar, explain why.
1)
5)
2
3)
6
8
4
3
12
6
Similar by AA Similarity.
2)
9
6
12
7)
4
3
12
9
8  4 , 12  4
10 5 15 5
Similar by SAS Similarity.
20
4)
3
15
12  4 , 9  3 , 6  2
15 5 12 4 9 3
Not Similar
3
20
Similar by AA Similarity.
6)
12
12
10
5
12  3 , 3
20 5 5
Similar by SSS Similarity.
Similar by AA Similarity.
8)
5
6
12
10
Not Similar
5
5
6.25 4
5 4
6.25 5
Similar by SAS Similarity.
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
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