Question

In a $\Delta ABC$, 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.

Answer 1

In $\Delta ABC$, BM and CN are perpendicular on a line drawn from A. L is the mid point of BC.

ML and NL are joined.

To prove : ML = NL

Proof : Consider two triangle $\Delta BLM$ and $\Delta CLN$
$\angle BML=\angle CNL={90}^{\circ }$
BL=LC as L is a mid point BC.
$\angle MLB=\angle NLC$ as vertically opposite angles.
Therefore, $\Delta BLM\cong \Delta CLN$.
Hence, LM=LN as corresponding sides of congruent triangles are equal.