plete the following proofs using the most appropriate method (SSS or SAS). en: overline(A B) cong overline(D E), overline(A B) | overline(D E), C is the midpoint of overline(A E) ve: triangle A B C cong triangle E D C STATEMENTS & & REASONS overline(B cong D E) & 1. & choose your answer... & checkmark |overline(D E) & 2. & choose your answer... & checkmark B A C cong angle D E C & 3. & choose your answer... & checkmark is the midpoint of overline(A E) overline(A C) cong overline(C E) & 4. & choose your answer... & checkmark triangle A B C cong triangle E D C & 5. & choose your answer... & checkmark

Question

Answer 1

To complete the proof, we will fill in the reasons for each statement step by step.Step 1:

Reason: Given.Step 2:

Reason: Given.Step 3:

Reason: Alternate Interior Angles are congruent when two lines are parallel and cut by a transversal (in this case,

is the transversal).Step 4:

is the midpoint of

Reason: Given.Step 5:

Reason: Definition of a midpoint (a midpoint divides a segment into two congruent segments).Step 6:

Reason: Side-Angle-Side (SAS) Postulate. We have two pairs of sides that are congruent (

and

) and the angle between them (

) is also congruent.Final Answer: The proof is completed using the SAS Postulate for congruence.

.

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