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In triangle abc, the median ad is perpendicular to BC. Prove that ABC is a isosceles triangle .

Answer»

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

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