Exams › SSC CGL (Prelims) › General

In \(\triangle ABC\), \(AD\) is the perpendicular bisector of \(BC\). Are triangles \(ABD\) and \(ACD\) congruent? If so, by what rule?

1. Yes, by SSS
2. Yes, by ASA
3. Yes, by SAS
4. No, they are not congruent

Correct answer: Yes, by SAS

Solution

Since \(AD\) is the perpendicular bisector of \(BC\), point \(D\) is the midpoint of \(BC\), so \(BD = DC\), and \(AD \perp BC\), giving \(\angle ADB = \angle ADC = 90^\circ\). Also, \(AD\) is common to both triangles. Thus, two sides and the included angle are equal, so the triangles are congruent by SAS.

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