Mathematics
In Δ ABC, AD is the perpendicular bisector of BC. Show that Δ ABC is an isosceles triangle in which AB = AC.
Triangles
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Answer
Given :
AD is the perpendicular bisector of BC.
∴ ∠ADB = ∠ADC = 90° and BD = DC.
In Δ ADC and Δ ADB,
⇒ AD = AD (Common side)
⇒ ∠ADC = ∠ADB (Each equal to 90°)
⇒ CD = BD (AD is the perpendicular bisector of BC)
∴ Δ ADC ≅ Δ ADB (By S.A.S. congruence rule)
We know that,
Corresponding parts of congruent triangles are equal.
∴ AB = AC (By C.P.C.T.)
Hence, proved that ABC is an isosceles triangle in which AB = AC.
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