 # Similarity Theorems.

## Presentation on theme: "Similarity Theorems."— Presentation transcript:

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 S V B 45 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. C U P T E A 32 16 12 28 21 TEA  CUP because of the SAS~ Postulate. 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 B Q R S 3 4 6 15 30 20 ABC  QRS because of the SSS~ Postulate. The scale factor is 1:5.

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

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

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

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.

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

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

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

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

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

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

Please complete the Ways to Prove Triangles Similar Worksheet.

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

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 B C D