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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Given : triangle ABC, AD is the perpendicular bisector of BC.
To Find : show that triangle ABC is an isosceles triangle in which AB=AC.
Solution:
AD is perpendicular bisector of BC
=> BD = CD
Also ∠BDA = ∠CDA = 90°
AD = AD common
=> ΔADB ≅ ΔADC ( SAS)
=> AB = AC
QED
Hence proved
triangle ABC is an isosceles triangle in which AB=AC.
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