Applying congruency and/or similarity to solve problems

• Vertical Angle theorem

• Alternate interior angle theorem

• Alternate exterior angle theorem

• SAS postulate

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.

ASA, AAS or Neither?

• ASA

• AAS

• Neither

Are the triangles shown congruent?

• Yes, by AAA

• Not enough information

• Yes, by ASA

• Yes, by AAS

Are the triangles congruent?

• Yes, by SSA≅

• Yes, by AAS≅

• Yes, by ASA≅

• Yes, by SAS≅

• Not enough information

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• SSA
• AAS
• ASA
• Not necessarily congruent

Given the diagram, which of the following is true?

• ∆XSF ≅ ∆XTG

• ∆SXF ≅ ∆GXT

• ∆FXS≅ ∆XGT

• ∆FXS ≅ ∆GXT

What property states that something is congruent to itself?

• Symmetry Property

• Congruence Property

• Reflexive Property

What shortcut would you use to prove the triangles congruent?

• SSS
• SAS
• ASA
• AAS

What is the reason for statement #1?

• Given

• $\overline{KM}\cong\overline{MK}$

• Definition of Congruent Segments

• Prove