Question

A conjecture 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 DF__________. So, DE________≅ by the definition of midpoint. Therefore, DE=EF by the ____________. DE+EF=DF by the segment___________ and so DE+DE=______________ by substitution. Simplifying gives 2DE=DF .

Answer choices:

Segment Congruence
segment Addition
DF
EF
DF
DE

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.

Answer 2

Answer:

OK here is the correct answer! Hope I helped! Sorry I am late! Really helpful for k12 students! Have a nice day!

Step-by-step explanation: