# Q: 4      Show that the diagonals of a square are equal and bisect each other at right angles.

Given : ABCD is a square i.e. AB=BC=CD=DA.

To prove : the diagonals of a square are equal and bisect each other at right angles i.e. AC=BD,AO=CO,BO=DO and

Proof : In BAD and ABC,

(Each )

AB=AB               (common)

BD=AC           (CPCT)

In AOB and COD,

OAB=OCD        (Alternate angles)

AB=CD               (Given )

OBA=ODC       (Alternate angles)

AOB  COD   (By AAS)

AO=OC ,BO=OD           (CPCT)

In AOB and AOD,

OB=OD        (proved above)

OA=OA          (COMMON)

AOB  AOD   (By SSS)

AOB=AOD           (CPCT)

AOB+AOD =

2. AOB =

AOB =

Hence,  the diagonals of a square are equal and bisect each other at right angles.

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