Triangles Chapter of Plane Geometry

Question

If AD is the altitude through A of triangle ABC, prove that AB > AC, AB = AC or AB < AC according as BD > DC.,BD = DC or BD < DC

Answer 1

Hint:

Use Pythagoras theorem in the two triangles, namely $\triangle ABD$ and $\triangle ADC$, to obtain the result.

In $\triangle ABD$,

$$AB^2 = AD^2 + BD^2$$

In $\triangle ADC$,

$$AC^2 = AD^2 + DC^2$$

Now subtract the two and make your observations.