Question

ABCD is a square. A is joined ta a point P on BC and D is joined to a point Q on AB . If AP=DQ ; prove that AP and DQ are perpendicular to each other.

Answer 1

This is the required answer

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

In ΔADQ and ΔAPB

AD = AB ( Sides of square are equal)

∠A = ∠B ( Each angle of square is right angle)

DQ = AP (Given)

So, By SAS congruency criterion, ΔADQ ≅ ΔAPB

⇒ ∠1 = ∠2 (Corresponding parts of the congruent triangles are equal)

Now, using angles sum property of triangle in ΔADM

∠1 + ∠3 + ∠4 = 180

⇒ ∠2 + ∠3 + ∠4 = 180 ( Because ∠1 = ∠2 )

But, ∠2 + ∠3 = 90

⇒ 90 + ∠4 = 180

⇒ ∠4 = 90°

Therefore, AP ⊥ DQ

Hence Proved.