Question

In a Δ ABC, M and N are the mid-points of AB and AC respectively. If BC=16 cm then find the length of MN. Is MN║BC

Answer 1

ANSWER

Given:- ABC is a △,M and N are the mid-points of AB and AC respectively. The altitude AP to BC intersect MN at O.

To prove:- AO=OP

Proof:-

Since M and N are the mid points of AB and BC,

By mid point Theorem,

MN∥BC

MN=

2

1

BC

Now In △ABP,

Since M is the mid point of AB,MO∥BP.

Therefore by Converse of midpoint theorem

O is the midpoint of AP

∴AO=OP

Hence proved.

Answer 2

Answer:

Given:- ABC is a △,M and N are the mid-points of AB and AC respectively. The altitude AP to BC intersect MN at O.

To prove:- AO=OP

Proof:-

Since M and N are the mid points of AB and BC,

By mid point Theorem,

MN∥BC

MN= 21

BC

Now In △ABP,

Since M is the mid point of AB,MO∥BP.

Therefore by Converse of midpoint theorem

O is the midpoint of AP

∴AO=OP