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 where applicable. Remember the Triangle Midsegment Theorem: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.

1. In triangle ABC, if D is the midpoint of AB and E is the midpoint of AC, what can you conclude about segment DE?

2. If a midsegment of a triangle measures 10 cm, the length of the third side (the base) is   cm.

3. A segment connecting the midpoints of two sides of a triangle is always   to the third side.

4. In triangle XYZ, M is the midpoint of XY and N is the midpoint of XZ. If YZ = 24 inches, what is the length of MN?

5. Consider a triangle with vertices at P(1, 2), Q(7, 2), and R(4, 8). Find the coordinates of the midpoints of PQ and QR. Then, find the length of the midsegment connecting these two midpoints and compare it to the length of PR.

6. The midsegment of a triangle is always longer than the third side.