In , let , and be the midpoints of sides , and…

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadrilaterals · Quadrilaterals

Problem

\triangle XYZ

, let

L

M

and

N

be the midpoints of sides

XY

YZ

and

ZX

respectively. (i) Prove that

LM \parallel XZ

MN \parallel XY

and

NL \parallel YZ

. (ii) Show that

\triangle LMN

is similar to

\triangle XYZ

. (iii) Prove that the area of

\triangle LMN

is one–quarter of the area of

\triangle XYZ