Advertisement Remove all ads

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM^2 = QM . MR - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR

Advertisement Remove all ads

Solution

Let ∠MPR =  x

In ΔMPR

∠MPR = 180º- 90º - x

∠MRP = 90º - x

Similarity, in ΔMPQ

∠MPQ = 90º - ∠MPR

= 90º - x

∠MQP = 180º - 90º - (90º - x)

∠MQP = x

In ΔQMP and ΔPMR

 ∠MPQ = ∠MRP

∠PMQ = ∠RMP

∠MQP = ∠MPR

∴ΔQMP ~ ΔPMR (By AAA Similarity criterion)

`=>(QM)/(PM) = (MP)/(MR)`

=>PM2 = QM x MR

Concept: Right-angled Triangles and Pythagoras Property
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.5 | Q 2 | Page 150

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×