Question

$AB$ is a line segment, $AX$ and $BY$ are two equal line segments drawn opposite sides of line $AB$, such that $AX\parallel BY$. If $\Delta APX\cong \Delta BPY$ then, line segments $AB$ and $XY$ intersect each other at point $P$ such that:

• A. Line Segment $AB$ and $XY$ are Perpendicular.
• B. Line Segment $AB$ and $XY$ are parallel.
• C. line segments $AB$ and $XY$ bisect each other at point $P$
• D. None

Answer 1

The correct option is C line segments $AB$ and $XY$ bisect each other at point $P$

Given $\Delta APX\cong \Delta BPY$.

So all three sides and angles of one triangles is equal to corresponding sides and angles of other triangle.

Then, $AP=PB$, i.e. $P$ bisects $AB$.

Similarly, $XP=PY$, i.e. $P$ also bisects $XY$.

From these two equations we can say that $AB$ and $XY$ bisect each other at point $P$.

Hence, option $C$ is correct.