In ( ABC ), points (D ) and (E ) are the midpoints of sides (AB ) and (AC )…

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

Problem

\triangle ABC

, points

D

and

E

are the midpoints of sides

AB

and

AC

respectively. (i) State the theorem that relates the segment joining

D

and

E

with the third side

BC

of the triangle. (ii) Using only geometric reasoning, explain why

DE \parallel BC

. (iii) Explain why

DE = \dfrac{1}{2}\,BC