In Fig. 10.99, AD ⊥ CD and CB ⊥ CD . If AQ = BP and DP = CQ , prove that ∠ DAQ = ∠ CBP.

Question

In Fig. 10.99, AD &#x22A5; CD and CB &#x22A5; CD . If AQ = BP and DP = CQ , prove that &#x2220; DAQ = &#x2220; CBP.

Philoid · Accepted Answer

Given that in figure,

AD ⊥ CD and CB ⊥ CD

And,

AQ = BP, DP = CQ

WE have to prove that,

∠DAQ = ∠CBP

Given that, DP = QC

Adding PQ on both sides, we get

DP + PQ = PQ + QC

DQ = PC (i)

Now consider , we have

∠ADQ = ∠BCP = 90^o (Given)

AQ = BP (Given)

And,

DQ = PC (From i)

So, by RHS congruence rule, we have

Now,

∠DAQ = ∠CBP (By c.p.c.t)

Hence, proved