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11/07/2021 12:17 pm
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In ΔABC, AD is the perpendicular bisector of BC (see Fig.). Show that ΔABC is an isosceles triangle in which AB = AC.
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11/07/2021 12:18 pm
It is given that AD is the perpendicular bisector of BC
To prove:
AB = AC
Proof:
In ΔADB and ΔADC,
AD = AD (It is the Common arm)
ADB = ADC
BD = CD (Since AD is the perpendicular bisector)
So, ΔADB ΔADC by SAS congruency criterion.
Thus,
AB = AC (by CPCT)