Similarity Theorems
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Transcript of Similarity Theorems
![Page 1: Similarity Theorems](https://reader036.fdocuments.us/reader036/viewer/2022062407/56812d5b550346895d926378/html5/thumbnails/1.jpg)
SIMILARITY THEOREMS
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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.
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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.
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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.
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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
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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
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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
![Page 8: Similarity Theorems](https://reader036.fdocuments.us/reader036/viewer/2022062407/56812d5b550346895d926378/html5/thumbnails/8.jpg)
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
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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
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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
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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
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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
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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
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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
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Please complete the Ways to Prove Triangles Similar Worksheet.
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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
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Theorem
If three parallel lines intersect two transversals, then the segments
intercepted are proportional.
a
b
c
d
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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
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Please complete pg. 449: 1-24, 31-33.