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A B is a line segment. A X\ a n d\ B Y a...

`A B` is a line segment. `A X\ a n d\ B Y` are two equal line segments drawn on opposite sides of line `A B` such that `A X||B Ydot` If `A B\ a n d\ X Y` intersect each other at `P ,`prove that ` A P X~=B P Y` (ii) `A B\ a n d\ X Y` bisect each other.
In the given figure, segment `AX and BY` are equa

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In the given figure, segment `AX and BY` are equal
`AX∣∣BY`,The line segment `AX∣∣BY` and line segment AB join the parallel line at A and B.
And line segment XY cut line AB at point P.
Then, in `/_\AXP and /_\PYB`
`AX=BY`..(Given)
`/_XAP(3)=/_YBP(4)(Adjacent angle)`
`/_AXP(1)=/_PYB(2) (Adjacent angle )`
Then`/_\APX~=/_\BPY`
`/_\APX~=/_\BPY,Then AP=BP andXP=PY`
Thus, the line segment AB and XY bisect each other.
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