Answer:
1. MN≅QP
MQ≅NP
2. MP≅MP
3. SSS congruence postulate
4. ∠N≅∠Q
5. CPCTC
Step-by-step 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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