Question

Prove that angle ABC is isosceles if median AD is perpendicular to BC..

Answer 1

Answer:

Consider triangles ABD and ACD.

As AD is a median of ABC, D is the midpoint of BC.  So BD = CD.

The side AD is common to both triangles.

If AD is perpendicular to BC, then ∠ADB = 90° = ∠ADC.

So by the SAS rule, triangles ABC and ACD are congruent.

Therefore AB = AC.

It follows that ABC is isosceles.

Answer 2

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