Question

In the figure below, AD is the perpendicular bisector of CB. Based on this information, which other statement can be proven to be

true?
OA AB AC
OB. AB CB
OCAC CB
OD AD CB
A
C
D
B

Answer 1

463833

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Medium

Solution

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In △ABD and △ACD, we have

DB=DC ∣ Given

∠ADB=∠ADC ∣ since AD⊥BC

AD=AD ∣ Common

∴ by SAS criterion of congruence, we have.

△ABD≅△ACD

⇒AB=AC ∣ Since corresponding parts of congruent triangles are equal

Hence, △ ABC is isosceles.

Answer 2

A.

Explanation:

With the given information, triangles ABD and ACD can be proved congruent, and by CPCTC, segments AB and AC are congruent.