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1.)Here BP and CP are the bisectors of ∠B and ∠C respectively.
And LM∥BC
Now ; ∠LPB = ∠CBP {alt. interior angle)
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.
And LM∥BC
Now ; ∠LPB = ∠CBP {alt. interior angle)
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.
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poorvi01:
Thanks A Lot
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