Question

ABCD is a rectangular figure in which DP and BQ a perpendicular from D and B respectively on diagonal AC.

Answer 1

This is the required answer to this question.

Answer 2

Step-by-step explanation:

Given that ,

(Refer the image attached)

DP and BQ are the perpendiculars on the diagonal AC

To prove :

(i) ΔADP ≅ ΔCBQ

From the figure we can observe that,

AD = BC (∵ opposite sides of a rectangle are equal)

∠DAP = ∠BCQ (Alternate angles)

∠DPA = ∠BQC (Both are equal to 90°)

∴ ΔADP ≅ ΔCBQ( by AAS (angle angle side) theorem)

=> CPCT(Corresponding parts of corresponding triangle) theorem states that two congruent triangles have congruent sides and congruent angles.

(ii) ∠ADP = ∠CBQ (by CPCT)

(iii) Line DP = Line BQ (by CPCT)

Hence proved