RM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. IF L is the mid-point of BC, prove that LM = LN.

Open in App

Solution

In BM and CN are perpendiculars on any line passing through A.

Also.

We need to prove that

From point L let us draw

It is given that , and

Therefore,

Since, L is the mid points of BC,

Therefore intercepts made by these parallel lines on MN will also be equal

Thus,

Now in ,

And . Thus, perpendicular bisects the opposite sides.

Therefore, is isosceles.

Hence

Hence proved.

Suggest Corrections

Similar questions

BM and CN are perpendicular to a line passing through the vertex A of a triangle ABC. If L is the mid-point of BC, prove that LM = LN.

BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If L is the mid point of BC, prove that LM=LN.

B M

and

C N

are perpendiculars to a line passing through the vertex

A

of a triangle

A B C

. If

L

is the mid-point of

B C

, then

L M = L N .

In a $Δ A B C$ , BM and CN are perpendiculars from B and C respectively on any line passing through A . If L is the mid-point of BC, prove that ML = NL.

Q. In a triangle ABC , BM and CM are perpendiculars from B And C respectively on any line passing through A If L is the midpoint of BC , prove that ML =NL

Join BYJU'S Learning Program