Question

triangle abc bisector of angle b and angle c meet at p through p a line lm is draw n parallel to bc meeting ab at l and ac at m show that lm = bl + cm​

Answer 1

Step-by-step explanation:

The figure below shows a triangle ABC;

Here BP and CP are the bisectors of ∠B and ∠C respectively.

And LM∥BC

Now ; ∠LPB = ∠CBP {alternate interior angles}

And ∠LBP = ∠CBP {given}

So; ∠LBP = ∠LPB

And we know that if the angles are equal then their corresponding sides are also equal.

Therefore; LP = LB

Similarly; MP = MC

So we have;

LP + MP = LB + MC

⇒LM = LB+MC

Hence proved.