Question

ABCD is a rectangle in which DP and BQ are the perpendiculars from D and B

respectively on the diagonal AC. Prove that DP = BQ.​

Answer 1

Step-by-step explanation:

write that since they are perpendicular from d and b to each other and since opposite sides of a rectangle are equal, the diagonals results to be equal and hence dp and bq are proved to be equal. hope it helps

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Answer 2

To prove:

• DP = BQ

Construction steps:

• Draw a rectangle ABCD.
• Draw a diagonal of the rectangle as AC.
• Draw BQ perpendicular to AC and PD perpendicular to BC.

Given:

• ABCD is a rectangle.

• Side AB = Side CD.

• Side AD = Side BC.

• DP is perpendicular from D and BQ is perpendicular from B.

Proof:

From the diagram,

⟹ ∠P = ∠Q = 90°

∴ ∆ADP and ∆CBQ are formed.

Now,

In ∆ADP and ∆CBQ,

⟹ ∠APD = ∠CBQ = 90°

⟹ ∠DAP = ∠BCQ ... {Alternate angles).

Therefore, ∆ADP ≅ ∆CBQ

∴ DP = BQ.

Hence proved.