Question

in ∆ ABC,AD is the perpendicular bisectors of BC. show that ∆ ABC is an isosceles triangle in which AB = AC. ​

Answer 1

GIVEN THAT:-

AB is perpendicular to BC

∆ABC is an isosceles triangle

TO PROVE:-

AB = AC

PROOF:-

$\large\sf{\angle{ADB}=\angle{ADC}(each\:of\:90°)}$

$\large\sf{BD=CD(AD\:is\:perpendicular\:bisector\:of\:BC)}$

$\large\sf{AD=AD(common)}$

$\therefore$ $\large\sf{∆ABD\:\cong\:∆ACD}$

By SAS congruence rule

$\large\sf{and\:AB=AC(CPCT)}$