Question

In A ABC, AD and BE are medians on sides BC and AC respectively. If angle DAC = CBE = 30° show that A ABC is an equilateral triangle.​

Answer 1

In triangles ADB & ADC

AD is median to BC (given)

=> BD = CD

& AD perpendicular to BC ( given)

=> <ADB = < ADC = 90°

& AD = AD ( common to both triangles)

=> tri ADB congruent to tri ADC ( by SAS congruence rule)

=> AB = AC ( csct)

Similarly, we can prove tri BEA congruent to tri BEC ( by SAS)

=> AB = CB ( csst)

This way AB = BC = AC

=> tri ABC is an equilateral triangle.