Question

in the diagram points D and E are midpoints of the sides as shown. Name two relationships between segment DE and segment BC.

Answer 1

Given

Triangle with midsegment

Procedure

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

First relation

$DE=\frac{1}{2}BC$

Second relation

$DE\Vert CB$

Conclusion: If the midpoints of any two sides of a triangle are joined by a segment, then that segment is parallel to the third side and half its length.