Question

Which of the following reasons could be used to correctly complete the proof? Select all that apply1.congruence of angles is reflexive2.congruence of angles is transitive3.congruence of angles is symmetric4. Definition of congruent triangles5.vertical angles are congruent

Answer 1

We have to prove that

The reflexive property refers to an angle is always congruent with itself. It does not apply in this case.

The transitive property refers that if a is congruent with b, and b is congruent with c, then a is congruent with c. This applies for the third row.

The symmetric property refers to if a is congruent with b, then b is congruent with a. This does not apply here.

The definition of congruent triangles (same angles and sides) does not apply here.

Vertical angles are congruent refers to the fact that angles that share a vertex and are opposite by that vertex are congruent.

For the second row (ABF congruent with BFE), we can apply both "vertical angles are congruent" (ABF congruent with CBD), Option 5, then we know that CBD is congruent with BFE (is given), so we can apply the transitive property (Option 2).

For the third row, we apply the transitive property again (Option 2), as CBD is congruent both with ABF and BFE.