1. Similarity Theorems

2. Similarity in Triangles
Angle-Angle Similarity Theorem (AA~)- If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. W R S V B
45
WRS  BVS because of the AA~ Theorem.

3. Similarity in Triangles
Side-Side-Side Similarity Theorem (SSS~)- If all three corresponding sides of two triangles are proportional, then the triangles are similar. C A B Q R S 3 4 6 15 30 20
ABC  QRS because of the SSS~ Theorem.
The scale factor is 1:5.

4. Similarity in Triangles
Side-Angle-Side Similarity Theorem (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. C U P T E A
32 16 12 28 21
TEA  CUP because of the SAS~ Theorem.
The scale factor is 4:3.

5. Are the following triangles similar
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

6. Are the following triangles similar
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 I 6 10 3 4
No, these are not similar because

7. Are the following triangles similar
Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A 20 25 X Y 25 30 B C
No, these are not similar because

8. Are the following triangles similar
Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. A P J B C 3 5 2 8
Yes, APJ  ABC because of the SSS~ Postulate.

9. Explain why these triangles are similar. Then find the value of x.
4.5 3 5 x
These 2 triangles are similar because of the AA~ Postulate.
x=7.5

10. Explain why these triangles are similar. Then find the value of x.5 x
70
110 3 3
These 2 triangles are similar because of the AA~ Postulate.
x=2.5

11. Explain why these triangles are similar. Then find the value of x.24 14 22
These 2 triangles are similar because of the AA~ Postulate.
x=12

12. Explain why these triangles are similar. Then find the value of x.6 9 2 x
These 2 triangles are similar because of the AA~ Postulate.
x= 12

13. Explain why these triangles are similar. Then find the value of x.4 5 x 15
These 2 triangles are similar because of the AA~ Postulate.
x=8

14. Explain why these triangles are similar. Then find the value of x.
7.5 12 18
These 2 triangles are similar because of the AA~ Postulate.
x= 15

15. Please complete the Ways to Prove Triangles Similar Worksheet.

16. Similarity in Triangles
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.
You can either use or T S U R V x 5 16 10

17. Theorem
If three parallel lines intersect two transversals, then the segments intercepted are proportional. a b c d

18. 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 B C D

19. Please complete pg. 449: 1-24,