Triangle Congruence Proofs Quiz with CPCTC Solutions

Question 1

In a two-column proof, you have: $AB \cong AB$. What is the correct reason?

Accepted Answer

Reflexive Property of Congruence

Answer

Transitive Property of Congruence

Answer

Symmetric Property of Congruence

Answer

Definition of Congruent Segments

Question 2

Overlapping triangles: In quadrilateral $ABCD$, diagonal $AC$ is drawn. Given $AB \parallel CD$ and $BC \parallel AD$. Which statement is true and helps prove $	riangle ABC \cong 	riangle CDA$?

Accepted Answer

$\angle BAC \cong \angle DCA$ (alternate interior angles)

Answer

$AB \cong CD$ (parallel lines imply congruent segments)

Answer

$\angle ABC \cong \angle CDA$ (vertical angles)

Answer

$AC \cong BD$ (diagonals are always congruent)

Question 3

Harder overlap/strategy: In triangle $ABC$, point $D$ lies on $AC$. Given $BD$ bisects $\angle ABC$ and $AB \cong CB$. Which method is most efficient to prove $AD \cong DC$?

Accepted Answer

Prove $	riangle ABD \cong 	riangle CBD$ by SAS, then use CPCTC

Answer

Use the Pythagorean Theorem in $	riangle ABD$ and $	riangle CBD$

Answer

Use SSA because you know two sides and a non-included angle

Answer

Conclude $AD \cong DC$ immediately from $AB \cong CB$

Triangle Congruence Proofs Quiz with CPCTC Solutions

Master Math with AI

Learning Resources

Trusted & Recognized