Question

PQR is a triangle in which PQ=PR. QM and RN are tge medians of the triangle. Prove that triangle NQR is congruent to triangle MRQ

Answer 1

Answer:

NQR is congruent to MQR

Step-by-step explanation:

Given:

• PQR is a triangle
• PQ=PR
• QM and RN are two medians

To Prove:

• NQR is congruent to MRQ

proof:

PQ = PR (Given)

so, angle PRQ = angle PQR(angle opposite to equal sides are also equal)

• given PQ=PR. --------1
• PN=NQ and PM =RM -------2(QM and RN are median)
• From 1 and 2
• PN+ NQ=PM+MR
• 2QN=2MR
• QN=MR

In triangle NQR and MRQ

angle PRQ= angle PQR

QN=MR

QR=QR(common)

NQR is congruent to triangle MRQ by side angle side criteria