Question

pqr is a triangle right angled at P and M is a point on QR such that PM is perpendicular to QR show that PM square is equals to QM into MR​

Answer 1

Question:

PQR is a triangle right angled at P and M is a point on QR such that PM is perpendicular to QR. show that PM^2 = QM × MR.

Refer to the attachment for figure

Solution:

We know the theorem that,

If a perpendicular is drawn on hypotenuse from the 90 degree vertex then the triangles on both side of this perpendicular are similar to each other.

therefore,

∆ PMR ~ ∆ QMP

so,

PM /QM = MR / PM

( being corresponding parts of similar triangles)

cross multiplying we will get

PM^2 = MR × QM

Hence proved.