devarshi-dt-logo

Question:

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

Solution:

In ΔABD and ΔACD, we have
DB=DC Given
∠ADB=∠ADC since AD⊥BC
AD=AD Common
∴ by SAS criterion of congruence, we have.
ΔABD ≅ ΔACD ⇒ AB=AC Since corresponding parts of congruent triangles are equal
Hence, ΔABC is isosceles.