Question

1. ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the
perpendicular bisector of BD.​

Answer 1

Answer:

is there any diagram????

Answer 2

Answer:

Hey mate, here is your answer.

Step-by-step explanation:

In the given image above.

AB = AD

and

DC = BC

Now,

in traingle ACD and ABC

AD= AB (given)

DC = BC (given)

AC = AC (common)

Therefore,

Triangle ADC is congruent to triangle ABC By SSA congurence criteria.

Therefore,

By C.P.C.T.

angle DAC = angle BAC

Now in Triangle AOD and triangle AOB

angle DAC = angle BAC (proved above)

AD = AB (given)

AO = AO (common)

Therefore,

both the given triangles are congruent by SAS criteria.

now,

By CPCT

DO = OB

Angle AOD = angle AOB

by using linear pair,

angle AOD + angle AOB = 180°

(as both the angles are equal )

2 angle AOD = 180°

angle AOD = 90°

Similarly,

angle AOB = 90°.

Using the same technique,

In triangle DOC and BOC.

AO= OC

angle DOC = angle BOC = 90°

Hence, proved.

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