Question

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

Answer 1

To prove - 1. AC = BD
2. diagonals bisect each other at 90°

Proof - In ACD and BDC

AD = BC (given)
angle D = angle C = 90° (angles of a square are of 90°)
DC = CD ( common side)
Under SAS
ACD is congruent to BDC

so, AC = BD (cpct)

In AOB and DOC

angle AOB = angle DOC ( V.O.A.)
AB = DC ( given)
angle ABD = angle CDO ( A.I.A.)

under ASA
AOB is congruent to DOC

OB =OD (given)
OA = OC ( given)

diagonals bisect each other hence proved
then In AOB and COB

AB = BC ( sides of a square are equal)
OB= OB ( common)
OA = OC (. proved above)
under SSS
AOB = COB

AOB + COB= 180°
AOB + AOB = 180° (AOB = COB)
2AOB = 180°
AOB = 180/2= 90°
hence proved

Answer 2

Answer:

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