Midsegment of a Triangle Worksheet

Midsegment of a Triangle

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Define what a midsegment of a triangle is and state its two key properties.

2. In triangle ABC, if DE is a midsegment parallel to BC, and BC = 18 cm, what is the length of DE?

3. Consider triangle XYZ with vertices X(1, 2), Y(7, 2), and Z(4, 8). Find the coordinates of the midpoints of sides XY and XZ. Let these midpoints be M and N respectively. Then, find the length of MN and YZ. Verify the Midsegment Theorem.

4. A midsegment of a triangle is a segment connecting the   of two sides of the triangle.

5. The length of a midsegment is   the length of the third side of the triangle.

6. A midsegment is always   to the third side of the triangle.

7. Every triangle has exactly three midsegments.

8. If a segment connects the midpoints of two sides of a triangle, it is always longer than the third side.

9. In the triangle below, D, E, and F are the midpoints of sides AB, BC, and AC respectively. If AB = 10 cm, BC = 12 cm, and AC = 14 cm, find the perimeter of triangle DEF.