Exploring Triangle Congruence Proofs: ASA, SAS, & SSS

The video tutorial covers triangle congruence using ASA, SAS, and SSS postulates. It includes four examples, each demonstrating a different postulate. The lesson aims to help students determine triangle congruence and understand the reasoning behind it. The teacher guides students through proofs, encouraging them to think critically about the statements and reasons involved.

What is the essential question for the unit on triangle congruence?

• How does algebraic knowledge of lines help to solve problems about geometric concepts?

• What are the properties of congruent triangles?

• What is the relationship between angles and sides in a triangle?

• How can we use the Pythagorean theorem in geometry?

Which postulate is used to prove that two triangles are congruent if two angles and the included side are known?

• SAS

• ASA

• AAS

• SSS

In the first proof example, which property is used to state that QP is congruent to QP?

• Symmetric Property

• Transitive Property

• Reflexive Property

• Substitution Property

What is the reason given for AE being congruent to CE in the second proof example?

• Alternate Interior Angles Theorem

• Vertical Angles Theorem

• Definition of Midpoint

• Reflexive Property

Which theorem states that vertical angles are congruent?

• Corresponding Angles Postulate

• Vertical Angles Theorem

• Same-Side Interior Angles Theorem

• Alternate Interior Angles Theorem

In the third proof example, what is the reason for stating that WX is congruent to YX?

• Vertical Angles Theorem

• Given

• Reflexive Property

• Definition of Midpoint

What postulate is used to prove the congruence of triangles in the third proof example?

• SSS

• AAS

• ASA

• SAS

In the fourth proof example, which property is used to state that AC is congruent to AC?

• Substitution Property

• Reflexive Property

• Transitive Property

• Symmetric Property

What postulate is used to prove the congruence of triangles in the fourth proof example?

• SSS

• SAS

• AAS

• ASA

What should be the final statement in a proof when proving triangle congruence?

• The definition of midpoint

• The reflexive property

• The congruence of the triangles

• The given information