Question

You areworking on a proof. You know that A and B are on the perpendicular bisector of line CD. What can you conclude. A) AC=BD. B) CB=AD. C) AC = AD. D) AB= CD

Answer 1

I think the answer is D) AB=CD. ☻♥

Answer 2

Answer: (C) is the right answer.The conclusion is AC = AD.

Explanation:

Let CD be any line and AB be the perpendicular bisector of CD bisects at O;i.e CO=OD...(1)

(with reference to the figure attached to the answer)

Construct two triangles ΔAOC and ΔAOD by joining A and C and A to D.

Then in ΔAOC and ΔAOD

CO=OD [from (1)]

∠AOD=∠AOD[90°]

AO=AO[common]

by SAS congruence criteria

ΔAOC ≅ ΔAOD

⇒AC=AD (corresponding parts of a congruent triangle are equal)

Hence the conclusion is AC = AD.