Applying Congruency and/or Similarity to Solve Problems

What is the relationship between the triangles?

• Similar by AA∼

• Similar by SAS∼

• Similar by SSS∼

• Not Similar or Congruent

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

• AA~

• SAS~

• SSS~

• Not Similar

Which is not a triangle similarity theorem?

• ASA∼

• SAS∼

• SSS∼

• AA∼

State if the triangles are similar by SAS.

• Similar but not SAS

• Yes, SAS Similarity

• Not similar.

State if the two triangles are similar by AA.

• Not Similar

• Similar but not by AA

• Similar by AA

The triangles are similar by...

• SAS

• AA

• ASA

• SSS

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

• AA

• SAS

• SSS

• Not Similar

Solve for x. 

• 8

• 6

• 10

• 12

What is the reason for statement #1?

• Given

• Definition of Congruent Segments

• Prove

Prove that Triangle ABC is congruent to Triangle DEF using the SSS (Side-Side-Side) congruence criterion.

• We can prove that Triangle ABC is congruent to Triangle DEF using the SSS criterion by showing that the length of side AB is equal to the length of side DE, the length of side BC is not equal to the length of side EF, and the length of side AC is equal to the length of side DF.

• We can prove that Triangle ABC is congruent to Triangle DEF using the SSS criterion by showing that the length of side AB is equal to the length of side DE, the length of side BC is equal to the length of side EF, and the length of side AC is equal to the length of side DF.

• We can prove that Triangle ABC is congruent to Triangle DEF using the SSS criterion by showing that the length of side AB is not equal to the length of side DE, the length of side BC is not equal to the length of side EF, and the length of side AC is not equal to the length of side DF.

• We can prove that Triangle ABC is congruent to Triangle DEF using the SSS criterion by showing that the length of side AB is equal to the length of side DE, the length of side BC is equal to the length of side EF, and the length of side AC is not equal to the length of side DF.