Question

Drag and drop a statement or reason to each box to complete the proof.

Given: parallelogram MNPQ


Prove: ∠N≅∠Q

Answer 1

1. MN≅QP

MQ≅NP

2. MP≅MP

3. SSS congruence postulate

4. ∠N≅∠Q

5. CPCTC

Explanation:

1. As per the property of parallelogram that opposite sides are congruent, in given case of parallelogram MNPQ the opposite sides

MN≅QP and MQ≅NP.

2. The reflexive property of congruence states that a line or a geometrical figure is reflection of itself and is congruent to itself. Hence in given case of parallelogram MNPQ

MP≅MP

3. SSS congruence postulate stands for Side-Side-Side congruence postulate, it states that when three adjacent sides of two triangle are congruent then the two triangles are congruent. In given case of parallelogram MNPQ, as the sides MN≅Q, MQ≅NP and MP≅MP hence

ΔMQP≅ΔPNM

5. As proven in part 4 that ΔMQP is congruent to ΔPNM, so as per the property of CPCTC (congruent parts of congruent triangles are congruent)

∠N≅∠Q

5. CPCTC stands for congruent parts of congruent triangles are congruent.

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