Question

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

Answer 1

hey the answer is ....

to prove that diagonals are equal...

consider triangle ADC AND BDC

AD = BC ( sides are equal )

angle D = angle C = 90'

DC = DC ( common base )

so by SAS PROPERTY traingle ADC AND BDC are congruent

AC = BD ( by cpct )

_____________

consider angle X AND X

ad them as they form linear pair

X + X = 180

2X = 180

X = 180/2

X =90'

THEREFORE they bisect at 90'


hope it helps uu frnd

Answer 2

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.