SIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity Postulate

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SIMILARITY THEOREMS

SIMILARITY THEOREMS

Similarity in Triangles Angle-Angle Similarity Postulate (AA~)- If two angles of one triangle are

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 45 R S 45 B V WRS BVS because of the AA~ Postulate.

Similarity in Triangles Side-Angle-Side Similarity Postulate (SAS~)- If an angle of one triangle is

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. 16 C T 32 28 12 E U P 21 TEA CUP because of the A SAS~ Postulate. The scale factor is 4: 3.

Similarity in Triangles Side-Side Similarity Postulate (SSS~)If the corresponding sides of two triangles are

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

Are the following triangles similar? If so, what similarity statement can be made. Name

Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. F J H G K Yes, FGH KJH because of the AA~ Postulate

Are the following triangles similar? If so, what similarity statement can be made. Name

Are the following triangles similar? If so, what similarity statement can be made. Name the postulate or theorem you used. M 6 O G 3 H R 10 No, these are not similar because 4 I

Are the following triangles similar? If so, what similarity statement can be made. Name

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

Are the following triangles similar? If so, what similarity statement can be made. Name

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

Explain why these triangles are similar. Then find the value of x. 4. 5

Explain why these triangles are similar. Then find the value of x. 4. 5 5 x 3 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

Explain why these triangles are similar. Then find the value of x. 5 x 70 3 110 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. x 24

Explain why these triangles are similar. Then find the value of x. 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

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

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. x 7.

Explain why these triangles are similar. Then find the value of x. x 7. 5 12 18 These 2 triangles are similar because of the AA~ Postulate. x= 15

Similarity in Triangles Side Splitter Theorem - If a line is parallel to one

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 You can either proportionally. use T x or S 16 R 5 U 10 V

Theorem Triangle Angle Bisector Theorem -If a ray bisects an angle of a triangle,

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 C D B