Answer:
1. QM≅RM
2. reflexive property of congruence
3. ΔPQM≅ΔPRM
4. SSS congruence postulate
5. CPCTC
Step-by-step explanation:
1. As M is the midpoint of line QR, dividing it in two equal parts that are QM and MR. Hence
QM≅RM
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,
PM≅PM
3. ΔPQM is congruent to ΔPRM because all the three sides PQ, QM and PM of ΔPQM are congruent to all the three sides PR, RM and PM of ΔPRM repectively.
4. 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, the three sides
PQ≅PR
QM≅RM
PM≅PM
hence ΔPQM ≅ΔPRM
5. CPCTC stands for congruent parts of congruent triangles are congruent. In given case as proven in part 4 that ΔPQM ≅ΔPRM so their corresponding angles will also be congruent. Hence
∠Q≅∠R
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