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