Question

A conjecture and the paragraph proof used to prove the conjecture are shown.

Answer 1

Observe the figure given.

Let us complete the given paragraph:

It is given that E is the midpoint of DF. So, DE $\cong EF$ by the definition of midpoint.

As, midpoint divides the line segment into two equal halves.

Therefore, DE  =EF by the segment congruence postulate. DE+EF = DF by the segment addition postulate and so DE+DE = DF by substitution.

Segment Addition Postulate states that given 2 points P and Q, a third point S lies on the line segment PQ if and only if the distances between the points satisfy the equation PS + SQ = PQ.

Simplifying gives 2DE = DF.