Question

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

A two-column proof of the theorem is shown, but the proof is incomplete.
Which of the following completes the proof?
Group of answer choices
a. By definition of congruence
b. Converse of corresponding angles postulate
c. By substitution
d. By construction

Answer 1

The completion of the proof is through construction (option d). By constructing the segment joining the midpoints of two sides of a triangle, we create two smaller triangles which are congruent by the Side-Angle-Side congruence postulate. Therefore, the segment joining the midpoints is parallel to the third side and half its length.

Step-by-step explanation:

The completion of the proof is through construction (option d). By constructing the segment joining the midpoints of two sides of a triangle, we create two smaller triangles. These smaller triangles are congruent to each other by the Side-Angle-Side (SAS) congruence postulate. Since the smaller triangles are congruent, their corresponding sides are also congruent, therefore, the segment joining the midpoints is parallel to the third side and half its length..