In the given figure, AB = AC. Prove that :

(i) DP= DQ

(ii) AP = AQ

(iii) AD bisects angle A

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Solution

Const: Join AD.

_{In triangke ABC
AB=AC
So Angle C=Angle B}

(i)

Angle BPD=Angle CQD
<B=<C
BD=DC
From AAS
_{Triangle BPD and CQD are congruent
So
DP=DQ}

(ii) We have already proved that _{Triangle BPD and CQD are congruent}

Therefore,BP = CQ[cpct]

Now,

AB = AC[Given]

AB - BP = AC - CQ

AP = AQ

(iii)

DP=DQ
AD=AD
AP=AQ
From SSS
Angle PAD=Angle QAD
Hence, AD bisects angle A.

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In the given figure, AB = AC. Prove that : (i) DP= DQ (ii) AP = AQ (iii) AD bisects angle A

In the given figure, AB = AC. Prove that :

(i) DP= DQ

(ii) AP = AQ

(iii) AD bisects angle A