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State whether the following statement is true or false.
If AD and BC are equal perpendiculars to a line segment AB (see figure), then CD bisects AB.

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True

False

answer is A.

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Detailed Solution

Given that,
AD and BC are equal (AD=BC) and perpendicular to a line segment AB.
Question Image

We know that the vertically opposite angles are equal.

Consider ∆OAD and ∆OBC,
Question Image

Thus, by AAS congruence rule:

We know that corresponding parts of congruent triangles are equal.

Hence, we can say that CD bisects AB.
Thus, the given statement is true.
So, option (1) is correct.

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