Question

ab = ac ad is bisector of angle a meeting bc at d prove abd conguunet adc and ad ⊥ bc

Answer 1

Given :-

• AB = AC
• AD is bisector of ∠A meeting BC at D

Required to prove :-

• ΔABD ≅ ΔACD
• AD ⊥ BC

Solution

• In ΔABD and ΔADC
• AB = AB  (given)
• ∠BAD = ∠DAC  (given)
• AD = AD  (common side)
• ∴ ΔABD ≅ ΔADC  (side angle side rule)
• ΔADB + ΔADC  (corresponding parts of congruent triangles)
• ∠ADB + ∠ADC = 180°  (linear pair)
• 2∠ADB = 180°
• ∠ADB = 180/2
• ∠ADB = 90°
• ∴ AD ⊥ BC

Answer 2

In ΔABD and ΔADC

AB = AB  (given)

∠BAD = ∠DAC  (given)

AD = AD  (common side)

∴ ΔABD ≅ ΔADC  (side angle side rule)

ΔADB + ΔADC  (corresponding parts of congruent triangles)

∠ADB + ∠ADC = 180°  (linear pair)

2∠ADB = 180°

∠ADB = 180/2

∠ADB = 90°

∴ AD ⊥ BC