Question

Write a two-column proof in the table provided at right. You may not need to use all the rows of the table for your proof.

Given: Angle MQP ≈ Angle NPQ, Angle MPQ ≈ angle NQP

Prove: Triangle MQP ≈ Triangle NPQ​

Answer 1

The two-column proves that ΔMNP ≅ ΔNPQ by the ASA Congruence Theorem is shown in the image attached below (see attachment).

What is the ASA Congruence Theorem?

The ASA congruence theorem states that two triangles that have two pairs of congruent angles and a pair of included congruent sides are considered congruent triangles.

We are given that both triangles have two pairs of congruent angles, by the reflexive property, we can state that QP ≅ QP in each triangle.

By this, it means both triangles have two pairs of congruent angles and a pair of congruent included sides. Therefore, ΔMNP ≅ ΔNPQ by the ASA Congruence Theorem.

Thus, the two-column proves that ΔMNP ≅ ΔNPQ by the ASA Congruence Theorem is shown in the image attached below (see attachment).

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