Mathematics

Problem

\triangle ABC

, points

D

and

E

are the midpoints of sides

AB

and

AC

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

D

and

E

with the third side

BC

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

DE \parallel BC

. c. (iii) Explain why

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