Question

Quadrilaterals
1)
ABC is an equilateral triangle, If AD is a median, prove that AD bisects angle A and
also AD is perpendicular to BC​

Answer 1

Hence proved

AD is angle bisector of ∠A

AD is perpendicular to BC

Step-by-step explanation:

Given: ABC is an equilateral triangle. AD is a median.

To prove: AD is bisects ∠A and AD is perpendicular to BC

Please see attachment for figure.

Proof:

In ΔBAD and ΔCAD

     BA = BA             ( side of same equilateral triangle)

     BD = CD             ( AD is a median)

     AD = AD             ( common side in both triangles)

∵  ΔBAD ≅ ΔCAD (By SSS congruence property )

∠BAD = ∠CAD   by CPCT (Congruent part of congruent triangle)

Therefore, AD is angle bisector of ∠A

∠BDA = ∠CDA   by CPCT (Congruent part of congruent triangle)

∠BDA + ∠CDA = 180°    ( Linear pair )

But ∠BDA = ∠CDA

Therefore, 2∠BDA = 180°

∠BDA = 90°

It means AD is perpendicular to BC

Hence proved

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