Question

Show that the diagonals of a square are equal and bisect each other at right angles.​

Answer 1

Mark me the brainliest please

Answer 2

☘️ Solution :

To prove :

• AC = BD
• ∠1 = ∠2 = ∠3 = ∠4 = 90°
• OA = OC, OB = OD

Proof :

In ∆ABC and ∆ABD

→ AB = AB (common)

→ AD = BC (side of square)

→ ∠A = ∠B [90°]

.°. ∆ABC ≅ ∆ABD (by SAS)

AC = AB [C.P.C.T]

Then,

In ∆AOD and ∆BOC

→ AB = DC (side of square)

→ ∠2 = ∠4 (vertically opposite angles)

→ ∠5 = ∠6 (alternate interior angle)

.°. ∆AOB ≅ ∆BOC (AAS)

OA = OC, OB = OD (C.P.C.T)

Now,

In ∆AOB and ∆BOC

→ OB = OB (common)

→ AB = BC (Side of square)

→ OA = OC (provide above)

.°. ∆AOB ≅ ∆BOC (SSS)

∠1 = ∠2 (C.P.C.T)

→ ∠1 + ∠2 = 180° (linear pair)

→ ∠1 + ∠1 = 180°

→ 2∠1 = 180°

→ ∠1 = 180/2

→ ∠1 = 90°

Similarly, ∠2 = ∠3 = ∠4 = 90°

Hence, proved.