In Fig., AD ⊥ CD and CB ⊥ CD. If AQ = BP and DP = CQ, prove that �

1.	In Fig., AD ⊥ CD and CB ⊥ CD. If AQ = BP and DP = CQ, prove that ∠DAQ = ∠CBP.
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, ΔDAQ and ΔCBP we have ∠ADQ = ∠BCP = 90°(Given) AQ = BP (Given) And, DQ = PC (From i) So, by RHS congruence rule, we have ΔDAQ ≅ ΔCBP Now, ∠DAQ = ∠CBP (By c.p.c.t) Hence, proved

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

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, ΔDAQ and ΔCBP we have

∠ADQ = ∠BCP = 90°(Given)

AQ = BP (Given)

And,

DQ = PC (From i)

So, by RHS congruence rule, we have

ΔDAQ ≅ ΔCBP

Now,

∠DAQ = ∠CBP (By c.p.c.t)

Hence, proved