Question

1. in △abc, d and e are midpoints of ab and ac, respectively. prove that de || bc. fill in the missing reason.

statement
d and e are midpoints of ab and ac
de = 1/2 bc
de || bc
reason
given
definition of midsegment
-

Explanation:

Step1: Recall the Midsegment Theorem

The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle (the midsegment) is parallel to the third side and half its length. In this case, since \(D\) and \(E\) are midpoints of \(AB\) and \(AC\) respectively, \(DE\) is the midsegment of \(\triangle ABC\).

Step2: Apply the Midsegment Theorem to the given statement

The statement \(DE\parallel BC\) and \(DE = \frac{1}{2}BC\) is a direct consequence of the Midsegment Theorem.

Answer:

d. Midsegment Theorem