Question

prove that triangle abc is an isosceles triangle, if median ad is perpendicular to the base bc​

Answer 1

Answer:

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.

Step-by-step explanation:

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=

2

180

=90°

∴∠ADB=∠ADC=90°