SIMILARITY THEOREMS
Similarity in Triangles
Angle-Angle Similarity Postulate (AA~)- If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
W
R
SV
B
4545
WRS BVS because of the AA~ Postulate.
Similarity in Triangles
Side-Angle-Side Similarity Postulate (SAS~)- If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the angles are proportional, then the triangles are similar.
TEA CUP because of the SAS~ Postulate.
C
U P
T
E A
3216 12
3228 21
The scale factor is 4:3.
Similarity in Triangles
Side-Side-Side Similarity Postulate (SSS~)- If the corresponding sides of two triangles are proportional, then the triangles are similar.
C
A
BQ
R S
3
4
6
1530
20
ABC QRS because of the SSS~ Postulate.
The scale factor is 1:5.
Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. F
G
H
K
J
Yes, FGH KJH because of the AA~ Postulate
Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used.M
O R
G
H I6
10
3
4
No, these are not similar because
Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A
X Y
B C
20
25
25
30
No, these are not similar because
Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used.
Yes, APJ ABC because of the SSS~ Postulate.
A
P J
B C
3
5
2
3
8
3
Explain why these triangles are similar. Then find the value of x.
3
5
4.5
x
These 2 triangles are similar because of the AA~ Postulate. x=7.5
Explain why these triangles are similar. Then find the value of x.
These 2 triangles are similar because of the AA~ Postulate. x=2.5
5
70 1103 3
x
Explain why these triangles are similar. Then find the value of x.
22
1424
x
These 2 triangles are similar because of the AA~ Postulate. x=12
Explain why these triangles are similar. Then find the value of x.
These 2 triangles are similar because of the AA~ Postulate. x= 12
x
6
29
Explain why these triangles are similar. Then find the value of x.
These 2 triangles are similar because of the AA~ Postulate. x=8
15
4
x
5
Explain why these triangles are similar. Then find the value of x.
These 2 triangles are similar because of the AA~ Postulate. x= 15
18
7.5 12
x
Please complete the Ways to Prove Triangles Similar Worksheet.
Side Splitter Theorem - If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
Similarity in Triangles
T
S U
R V
x 5
16 10
You can either use
or
Theorem
If three parallel lines intersect two transversals, then the segments
intercepted are proportional.
a
b
c
d
Theorem
Triangle Angle Bisector Theorem -If a ray bisects an angle of a triangle, then it divides the opposite side on the triangle into two segments that are proportional to the other two sides of the triangle. A
BC D
Please complete pg. 449: 1-24, 31-33.