Question

in the given figure triangle lmn is an isosceles triangle with l m is equal to Allen and LP bisect angle and I'll prove that all people with Aman

Answer 1

Can you Show The Figure

Answer 2

Given: triangle LMN is an isoceles triangle LM=Ln and lp bisects angle nlq
to prove:LM is parrallel MN
Proof: As LM =LN
so, Angle LNM=LMN..........side opposite to equal angle is equal .......1

Angle QLP=ANGLE PLN.........LP bisects Angle NLQ... 2

Now, by exterior angle property
Angle QLN=Angle LNM+ANGLE LMN......3
ANGLE PLM=1/2ANGLE LNM+1/2ANGLE LMN......4

Subtract 3 and 4
angle qln- angle PLM =angle lnm + angle lmn-(1/2ANGLE LNM+1/2ANGLE LMN)
ANGLE PLM=angle lnm + angle lmn-1/2ANGLE LNM-1/2ANGLE LMN
ANGLE PLM=angle lnm + angle lnm-1/2ANGLE LNM-1/2ANGLE LNM
ANGLE PLM=2angle lnm-1/2x2ANGLE LNM
ANGLE PLM=2angle lnm-ANGLE LMN
ANGLE PLM=ANGLE LMN

But these are alternate interior angle so by converse of alternate interior angle
LP is parrallel MN