Question

In ΔABC, AD is the perpendicular bisector of BC. Show that ΔABC is an isosceles triangle in which AB = AC.

Answer 1

Given :

• In ΔABC, AD is the perpendicular bisector of BC

To Prove :

• ΔABC is an isosceles triangle in which AB = AC.

Solution :

In ΔADC and ΔADB,

AD = AD (Common)

∠ADC =∠ADB (Each 90º)

CD = BD (AD is the perpendicular bisector of BC)

∴ ΔADC ≅ ΔADB (By SAS congruence rule)

∴AB = AC (By CPCT)

Therefore, ABC is an isosceles triangle in which AB = AC.

Figure (In attachment)