Question

The sides PQ ,PR of triangle PQR are equal and S,T are points on PR,PQ such that triangle PSQ and triangle PTR are right angles . Prove that the triangle PTR and Triangle pSQ are congruent and if QS and RT interest at M, prove that the triangle PTM and PSM are congruent.

Answer 1

in ptr and psq:
angle ptr= angle psq(90')
pr=pq(given)
angle p=angle p( common)
so, ptr is congruent to psq ( rhs)
pt=ps(cpct) ....(1)

in ptm and psm:
angle ptm= angle psm(90')
pm=pm(common)
pt=ps ....(from 1)
ptm is congruent to psm ( rhs)

so, I think this will be helpful.

Answer 2

here is your answer mate !! hope it helps you