Question

ABCD is a quadrilateral in which all the four angles, A = B and C=D. Show that AB||DC.

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Answer 1

Answer:

Solution:-

Given,

ABCD is a quadrilateral

Angles A=B=Ç=D

To Prove,

AB || CD and AD || BC

Proof:- Here,

angle A+B+Ç+D=360° [angle sum property of quadrilaterals]

=>A+A+A+A=360°

=>4A=360°

=>A=90° ……[equation 1]

Again, angle A+B=180°

Therefore, angles A and B are linear

And also they are adjacent.

Therefore, AD || BC because there interior angles A and B add up to 180°.

Similarly, angle A+D=180°

Therefore, angles A and D are linear

And also they are adjacent.

Therefore, AB || CD because there interior angles A and B add up to 180°.

Therefore, it is proved that AB ||CD

And AD || BC.

Answer 2

Solution:-

Given,

ABCD is a quadrilateral

Angles A=B=C=D

To Prove,

AB || CD and AD || BC

Proof:-

Here,

angle A+B+Ç+D=360° [angle sum property of quadrilaterals]

$\sf\implies$A+A+A+A=360°

$\sf\implies$4A=360°

$\sf\implies$A=90° ……[equation 1]

Again,

angle A+B=180°

Therefore, angles A and B are linear

And also they are adjacent.

And also they are adjacent.Therefore, AD || BC because there interior angles A and B add up to 180°.

Similarly, angle A+D=180°

Therefore, angles A and D are linear

Therefore, angles A and D are linearAnd also they are adjacent.

Therefore, angles A and D are linearAnd also they are adjacent.Therefore, AB || CD because there interior angles A and B add up to 180°.

Therefore, it is proved that AB ||CD

And AD || BC.