Krishna
0

Step 1: Use the given data to make a diagram.

GIVEN: ΔPQR is right angled at P is a point on QR such that PM ⊥QR.

Step 2: Prove that the triangles (PRM and PQM) are similar

NOTE:   \angle PMQ = \angle PMR = 90

\angle a + \angle b = 90.............(1)

\angle a +   \angle c = 180 - 90 = 90 ................(2)

From equation (1) and (2) we can write

\angle b =   \angle c

Similarly,   \angle a  =   \angle d

Therefore, by using the AA similarity

[math] \triangles PRM , \triangle PQM are similar

Step 3: Find the required ratio by  using the similar triangle properties.

EXAMPLE:  ΔPQM similar ΔPMR

Therefore,

The corresponding sides are proportional

\frac{QM}{PM} = \frac{PM}{RM}

Cross multiply

QM.RM = PM. PM

PM^2 = QM. RM