Question

In the figure, PQ is the bisector of ∟P, show that
a) PL > LQ
b) PM > QM

Answer 1

Step-by-step explanation:

refer the above attached figure

Answer 2

Step-by-step explanation:

Given :

PQ is bisector of angle LPM.

To prove :

(i) PL > LQ

(ii) PM > QM

Proof :

Since, PQ bisects angle LPM,

therefore, angle LPQ = angle MPQ = x ( let )

Let angle QLP = l and angle PMQ = m

angle PQL = x + m....(i) { Exterior angle }

Similarly, angle PQM = x + l....(ii)

Angle PQL > Angle LPQ

{ Since, angle PQL = x + m and angle LPQ = x }

therefore, PL > LQ.

{ Since, greater the angle, greater will be it's opposite side. }

Similarly, angle PQM > angle QPM

{ ang. PQM = x + l, ang QPM = x }

therefore, PM > QM.

Hence, proved.