Question

5. A triangle ABC has angle B = angle C.
Prove that :
(i) the perpendiculars from the mid-point of
BC to AB and AC are equal.
(ii) the perpendiculars from B and C to the
opposite sides are equal.​

Answer 1

Answer: Let's take a triangle ABC.   (See file attached below).

Let perpendicular from the mid-point of  BC to AB and AC be MO and NO.

Here, ∠B=∠C, Therefore the triangle ABC is isosceles, ∴AB=BC.

If M and N are midpoints on AB and AC, and then if AB=BC, then MC and NB are equal.

1. Now, In Triangles NBC and MBC,

∠B=∠C, ( given in question),

MC=NB, (Proved),

,CB=CB (Common).

Thus,  NBC ≅ MBC.

CPCT, MO=NO.

∴ the perpendiculars from the mid-point of  BC to AB and AC are equal.

2. Let the perpendiculars from B and C to the  opposite sides be MB and NC.

We proved that  NBC ≅ MBC.

CPCT, MB=NB.

∴the perpendiculars from B and C to the  opposite sides are equal.

HOPE IT HELPS :D

Answer 2

This is the right answer