In Δ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that Δ ABC is an isosceles triangle in which AB = AC.

Question

In &#x394; ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that &#x394; ABC is an isosceles triangle in which AB = AC.

Philoid · Accepted Answer

It is given in the question that:

AD is the perpendicular bisector of BC

To show: AB = AC

Proof: In

AD = AD (Common)

∠ADB = ∠ADC

BD = CD (AD is the perpendicular bisector)

Therefore,

By SAS congruence axiom,

AB = AC (By c.p.c.t)