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Solution for In Fig. 10.99, Ad ⊥ Cd and Cb ⊥. Cd. If Aq = Bp and Dp = Cq, Prove that ∠Daq = ∠Cbp. - CBSE Class 9 - Mathematics

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Question

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

 

Solution

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 

 

  Is there an error in this question or solution?

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Solution In Fig. 10.99, Ad ⊥ Cd and Cb ⊥. Cd. If Aq = Bp and Dp = Cq, Prove that ∠Daq = ∠Cbp. Concept: Criteria for Congruence of Triangles.
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