Aconjecture and the paragraph proof used to prove the conjecture are shown. drag an expression or statement to each box to complete the proof. it is given that e is the midpoint of so, ≅ by the definition of midpoint. therefore, de=ef by the de+ef=df by the and so de+de= by substitution. simplifying gives 2de=df . answer choices: segment congruence segment addition df ef df de

Observe the figure given.

Let us complete the given paragraph:

It is given that E is the midpoint of DF. So, DE 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.

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