Triangle Similarity Theorem and Review

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar

Review the picture. Find the missing side measurement in the picture using a proportion.

• x = 900 m

• x = 52 m

• x = 25 m

• x = 0.04 m

Why are the triangles similar?

• AA

• SAS

• SSS

• Not similar

The triangles are similar. State the reason and complete the similarity statement.

Answer explanation

The order of the points matter! The endpoints of the shortest sides have to line up! Same with the longest sides!

Match the following

• Triangle Proportionality Theorem

• If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

• SAS Similarity Theorem

• two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional

• AA Similarity Postulate

• two triangles are considered similar if at least two corresponding angles are congruent

• SSS Similarity Theorem

• in any triangle, if a line intersects two sides of the triangle and is parallel to the third, then the intersecting line divides the sides proportionally

• Angle Bisector Theorem

• an angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

• AA ~ Theorem

• SAS ~ Theorem

• SSS ~ Theorem

• Not similar

State if the triangles in each pair are similar. If so, state how you know.

• SSS ~

• SAS~

• AA~

• NOT ~

State if the triangles are similar by SAS.

• Yes, SAS Similarity

• Similar but not SAS

• Not Similar

Which theorem(s) can be used to prove triangle similarity?

• SAS

• AA

• AAS

• SSS

• HL

Find the missing side length.

• 9

• 6

• 8

• 7