Question

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

 

Answer 1

Given that, in the figure AD ⊥ CD and CB ⊥ CD and AQ = BP,DP =CQ 

We have to prove that ∠DAQ=∠CBP 

Given that DP= QC 

 Add PQ on both sides 

Given that DP=QC 

Add PQ on both sides 

⇒ DP+PQ=PQ+QC 

⇒ DQ=PC                 ................(1) 

Now, consider triangle DAQ and CBP,
We have 

∠ADQ=∠BCP=90°            [given]

AQ=BP                           [given] 

And DQ=PC                   [given] 

So, by RHS congruence criterion, we have ΔDAQ≅ΔCBP 

Now,  

∠DAQ=∠CBP         [ ∵Corresponding parts of congruent triangles are equal] 

∴ Hence proved