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Fifth Postulate and Playfair's Axiom

Two lines A B...

Question

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

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Solution

It is given that

We have to prove that the lines and bisect at.

If we prove that, then

We can prove and bisects at.

Now in and

(Given)

(Since and is transversal)

And (since and is transversal)

So by congruence criterion we have,

, so

Hence and bisect each other at.

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A B

C D

O

B C

is equal and parallel to

A D

A B

C D

Two lines AB and CD interest at O such tht BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

Let AB and CD be two line segments such that AD and BC intersect at O. Suppose AO = OC and BO = OD. Prove that AB = CD.

Q. In figure, two lines

A B

C D

intersect each other at the point

O

B C ∥ D A

O

is the mid-point of both the line-segments

A B

C D

.

Q. In fig 7.1, two lines AB and CD intersect each other at the point O such that

B C ∥ D A

B C = D A

.
Show that O is the mid point of both the line-segments AB and CD.

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Fifth Postulate and Playfair's Axiom

Standard IX Mathematics

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