in triangle ABC, AD is the perpendicular bisector of BC. show that triangle ABC is an isosceles triangle in which AB = AC.
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Step-by-step explanation:
AD is perpendicular bisector i.e. BD = DC and angle ADB = angleADC = 90°
Taking ∆ADB and ∆ADC
BD = DC
angle ADB = angleADC = 90°
AD = AD (common)
By S.A.S congruence rule,
∆ADB and ∆ADC are congruent triangles i.e.
AB = BC
HENCE,∆ABC IS AN ISOSCELES TRIANGLE.
PROVED.
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