Triangle Congruence Theorems and CPCTC Proofs

The video tutorial explains how to use CPCTC (Corresponding Parts of Congruent Triangles are Congruent) in two-column proofs. It reviews the four postulates needed to prove triangle congruence: SSS, SAS, ASA, and AAS. The tutorial provides several examples demonstrating how to apply CPCTC to prove congruence of angles and segments in various geometric configurations, including triangles, circles, and parallel lines.

Which postulate requires all three sides of two triangles to be congruent to prove the triangles are congruent?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

What does CPCTC stand for?

• Corresponding Parts of Congruent Triangles are Congruent

• Congruent Parts of Corresponding Triangles are Congruent

• Corresponding Parts of Congruent Triangles are Corresponding

• Congruent Parts of Corresponding Triangles are Corresponding

In the first example problem, which postulate is used to prove that triangle ABC is congruent to triangle DEF?

• Angle-Angle-Side (AAS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

What is the final step in a two-column proof after proving two triangles are congruent?

• Using CPCTC

• Using the Reflexive Property

• Using the Definition of Congruent Segments

• Using the Definition of Midpoint

In the second example problem, what property is used to show that BD is congruent to itself?

• Substitution Property

• Reflexive Property

• Symmetric Property

• Transitive Property

Which postulate is used in the second example problem to prove that triangle ABD is congruent to triangle CBD?

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

In the third example problem, what is the reason given for AE being congruent to DE?

• Definition of a midpoint

• Vertical angles are congruent

• Definition of congruent segments

• All radii of a circle are congruent

What is the reason for stating that angle AEB is congruent to angle DEC in the third example problem?

• Alternate interior angles are congruent

• Vertical angles are congruent

• Supplementary angles are congruent

• Corresponding angles are congruent

In the fourth example problem, which postulate is used to prove that triangle ACB is congruent to triangle ECD?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

What is the reason for stating that segment AC is congruent to segment CE in the fourth example problem?

• Definition of congruent segments

• All radii of a circle are congruent

• Definition of a midpoint

• Vertical angles are congruent