in triangle abc is bisect ad of angle a is perpendicular to side bc show that ab=ac and a bc is a isoceles
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Given: AD is a perpendicular bisector of BC
To Prove: <ABC is an isosceles triangle AB = BC
∴ AD is the perpendicular of BC
= <ADB = <ADC = 90
= BD = CD (AD is the bisector of BC)
=> Consider, ΔABD and ΔACD
= AD = AD (Common Side)
= <ADB = <ADC (AD is the perpendicular to BC)
= BD = CD (AD is the bisector of BC)
∴ By SAS Congruence rule,
= ΔABD ≅ ΔACD
= <B = <C (CPCT)
= AB = AC
= ΔABC is an isosceles triangle
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