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Question

In ABC,AD is the perpendicular bisector of BC (see given figure). Show that ABC is an isosceles triangle in which AB=AC
569813_78e1e4df5f7440eb9f3b98a65d066a79.png

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Solution

As AD is the perpendicular bisectorADB=900(1) and BD=DC(2)

In ΔADB and ΔADC

ADB=ADC=900 from 1

BD=DC From 2

AD is the common side.

ΔADBΔADC [by SAS congruence]

Thus sides AB=AC

i.e. ΔABC is isosceles triangle.

Hence Proved

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