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

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

Step-by-step 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.

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