in the given figure, MP = MQ. MR is the bisector of angle PMQ. Prove that ∆MPR ~= ∆MQR.Is angle P = angle Q?
Answers
PQR is an isosceles triangle with PQ = PR and M is the midpoint of QR. How do you prove that the line PM bisects <QPR?
We have two triangles PQM and PRM.
PQ = PR [given]
QM = MR [M being the midpoint of QR]
PM is common to both.
Hence the two triangles PQM and PRM are congruent [By SSS postulate]
Therefore <QPM = <RPM [ angles opposite equal sides QM and MR], so PM bisects the <QPR.
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Answer:
PQR is an isosceles triangle with PQ = PR and M is the midpoint of QR. How do you prove that the line PM bisects <QPR?
We have two triangles PQM and PRM.
PQ = PR [given]
QM = MR [M being the midpoint of QR]
PM is common to both.
Hence the two triangles PQM and PRM are congruent [By SSS postulate]
Therefore <QPM = <RPM [ angles opposite equal sides QM and MR], so PM bisects the <QPR.