Question

For which segment lengths is AC⎯⎯⎯⎯⎯ parallel to DE⎯⎯⎯⎯⎯? A triangle with vertices labeled as A, B, and C. Side AC is the base. Sides AB and BC contain midpoints D and E, respectively. A line segment drawn from D to E is labeled with a single arrowhead. Select Parallel or Not parallel for each set of given information.

a. Parallel
b. Not parallel

Answer 1

Segment AC is parallel to segment DE if and only if triangle ABC is an isosceles triangle.

Step-by-step explanation:

In order for segment AC to be parallel to segment DE, the triangle ABC must be an isosceles triangle with congruent sides AB and BC. This means that points D and E must be the midpoints of sides AB and BC, respectively. Therefore, segment AC is parallel to segment DE if and only if triangle ABC is an isosceles triangle.