Show that the diagonals of a square are equal and bisect each other at right angles. Question Show that the diagonals of a square are equal and bisect each other at right angles. in progress 0 Math Aubrey 1 week 2021-09-09T17:51:59+00:00 2021-09-09T17:51:59+00:00 2 Answers 0 views 0

## Answers ( )

Step-by-step explanation:Given that ABCD is a square.

To prove : AC=BD and AC and BD bisect each other at right angles.

Proof:

(i) In a ΔABC and ΔBAD,

AB=AB ( common line)

BC=AD ( opppsite sides of a square)

∠ABC=∠BAD ( = 90° )

ΔABC≅ΔBAD( By SAS property)

AC=BD ( by CPCT).

(ii) In a ΔOAD and ΔOCB,

AD=CB ( opposite sides of a square)

∠OAD=∠OCB ( transversal AC )

∠ODA=∠OBC ( transversal BD )

ΔOAD≅ΔOCB (ASA property)

OA=OC ———(i)

Similarly OB=OD ———-(ii)

From (i) and (ii) AC and BD bisect each other.

Now in a ΔOBA and ΔODA,

OB=OD ( from (ii) )

BA=DA

OA=OA ( common line )

ΔAOB=ΔAOD—-(iii) ( by CPCT

∠AOB+∠AOD=180° (linear pair)

2∠AOB=180°

∠AOB=∠AOD=90°

∴AC and BD bisect each other at right angles.

So here is your answer….

AC = BD

OA=OC

OB=OD

and angle AOB 90′

Hence The diagonals of a square are equal in length and the diagonals are bisect each other…

Ihopethatitgonnahelpyou