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

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

We have to prove that ∠DAQ=∠CBP

Now, consider triangle DAQ and CBP,

We have

So, by RHS congruence criterion,

we have ΔDAQ≅ΔCBP


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

∴ Hence proved

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