Triangle Congruence Proofs: CPCTC and Beyond

The video tutorial guides geometry students through understanding and solving geometric proofs. It begins with an introduction to the components of a proof, including diagrams, statement-reason tables, and given information. The instructor then walks through two detailed examples: proving angle congruence using side-side-side and corresponding parts of congruent triangles, and proving triangle congruence with overlapping triangles using the side-angle-side theorem. The tutorial emphasizes visualization, marking diagrams, and understanding geometric properties to build formal arguments.

What are the common components of every proof?

• Only a statement-reason table and what needs to be proven

• Only a diagram and given information

• None of the above

• Diagram, statement-reason table, given information, and what needs to be proven

What is the first given information in the proof that angle C is congruent to angle B?

• Angle C is congruent to angle B

• Segment CD is congruent to segment BD

• Segment AB is congruent to segment AC

• Segment AD bisects segment CB

What property is used to state that segment AD is congruent to itself?

• Symmetric Property

• Addition Postulate

• Transitive Property

• Reflexive Property

Which theorem is used to conclude that triangle ACD is congruent to triangle ABD?

• Side-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

• Angle-Angle-Side

What is the final reason given to prove that angle C is congruent to angle B?

• Reflexive Property

• Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

• Addition Postulate

• Base Angle Theorem

What is the first given information in the proof that triangle GEJ is congruent to triangle FEH?

• Segment GH is congruent to segment FJ

• Angle EHG is congruent to angle EJ F

• Segment HJ is congruent to itself

• Segment GJ is congruent to segment FH

What property is used to state that segment HJ is congruent to itself?

• Addition Postulate

• Transitive Property

• Reflexive Property

• Symmetric Property

Which postulate is used to combine congruent segments to form the base of each triangle?

• Addition Postulate

• Division Postulate

• Multiplication Postulate

• Subtraction Postulate

What theorem is used to state that the sides opposite the congruent angles in an isosceles triangle are also congruent?

• Side-Angle-Side Theorem

• Base Angle Theorem

• Angle-Side-Angle Theorem

• Side-Side-Side Theorem

Which theorem is used to conclude the proof that triangle GEJ is congruent to triangle FEH?

• Side-Angle-Side Theorem

• Angle-Side-Angle Theorem

• Side-Side-Side Theorem

• Angle-Angle-Side Theorem