Question

In a figure AP and BQ are perpendicular to the line segment AB and AP=BQ. Prove that 'O' is the midpoint of line segment AB as well PQ.

Answer 1

This is your answer.Hope it helps.

Answer 2

O is the midpoint of the line segment AB when AP and BQ are perpendicular to the line segment and AP=BQ.

Given that,

In the figure we have 2 triangles ΔAOP and ΔOBQ

The line segments AB and AP =BQ are perpendicular to AP and BQ.

We have to find that O is the midpoint of line segment AB as well PQ.

We know that,

In ΔOAP and ΔOBQ,

AP=BQ

∠OAP=∠OBQ=90°

∠OAP=∠OBQ (vertically opposite angles)

ΔOAP is congruent to ΔOBQ by AAS axiom (Angle-angle-side rule)

OA=OB and OP= OQ

Therefore, O is the midpoint of the line segment AB when AP and BQ are perpendicular to the line segment and AP=BQ.

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