Question

prove that tirangle is an isosceles triangle,if median ad perpendicular to bc

Answer 1

SOLUTION

Let ABC is an isosceles triangle with AB=AC and let AD be the median to the base BC

Then D is the mid-point of BC.

$ΔABD≅ΔADC \:  by \: SSS$

SO,

$∠ADC=∠ADB=x$

$∴∠ADB+∠ADC=180$

$x+x=180$

$x = \frac{180}{2} = 90$

$∴∠ADB=∠ADC=90∘$

Therefore AB = AC.

It follows that ABC is isosceles.