Similarity and Congruence of Triangles Review. What are the 3 theorems for similarity?

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Presentation transcript:

Similarity and Congruence of Triangles Review

What are the 3 theorems for similarity?

Are the triangles similar? If so, how?

Are the triangles similar? If so, how??

Are the triangles similar? If so, how??

Are the triangles similar? AC = 10, BC = 6, DE = 30, EF = 18, and <C = < E

Using Similarity Theorems A B In the diagram, EC = DC CA BC E D C What other information would you need in order to prove CDE is similar to CBA using Side-Angle-Side similarity?

Find x. The triangles below are similar.

Find x. The triangles to the right are similar.

Find x. The triangles to the right are similar.

Find x. The triangles to the right are similar.

Find the length of AC. ADE ~ ABC

Using similar triangles A fence post is 6 feet tall and casts a shadow 2.5 feet long. A nearby barn casts a shadow 8 feet long. How tall is the barn?

Using similar triangles ADE ~ ABC. If AD is 4 units long, AB is 12 units long, and the area of ADE is 20 square units, what is the area of ABC?

Using similar triangles x + 1 S Using the figure below, find x. R 6 T QP

CONGRUENCE What are the 5 congruence theorems for triangles?

Using Congruent Triangles Using SAS Congruence, and given that AB = XY and <A = <X, give the other piece of information needed to prove Δ ABC = Δ XYZ.

Are the triangles congruent? Determine which postulate can be used to prove that the triangles are congruent. If it is not possible, write “not possible”.

Are the triangles congruent? Determine which postulate can be used to prove that the triangles are congruent. If it is not possible, write “not possible”.

Are the triangles congruent? Determine which postulate can be used to prove that the triangles are congruent. If it is not possible, write “not possible”.

Triangle Centers What point of concurrency is shown in the picture below?

Triangle Centers What point of concurrency is shown in the picture below?

Triangle Centers What point of concurrency is shown in the picture below?

Triangle Centers What point of concurrency is shown in the picture below?

Triangle Centers If AG has a length of 18, what are the lengths of GH and AH? H

Vertical Angles Find the value of x. 5x x – 9

Angles formed by Transversals Find the values of x and y. 5y 5x x + 15