Mid-Segment of a Triangle Topic Index | Geometry Index | Regents Exam Prep Center

 Definition:
The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.

 Properties:

1.

The mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle.

2.

The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle.

 Examples:
1. Given DE is the length of the mid-segment.  Find AB.   Solution:
The mid-segment is half of the third side.
7 is half of 14.
AB = 14.

2. Given DE, DF, and FE are the lengths of mid-segments.  Find the perimeter of triangle ABC.   Solution:
The mid-segment is half of the third side.
6 is half of 12 so AC = 12
7 is half of 14 so CB = 14
8 is half of 16 so AB = 16
The perimeter of the large triangle ABC is:
12 + 14 + 16 = 42.

3.

 Statements Reasons 1. 1. Given 2. 2. The mid-segment of a triangle is parallel to the third side of the triangle. 3. 3. If two parallel lines are cut by a transversal, the corresponding angles are congruent. 4. 4. Transitive property. 5. 5. The midpoint of a segment divides the segment into two congruent segments. 6. 6. AAS.  If 2 angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

 Topic Index | Geometry Index | Regents Exam Prep Center Created by Donna Roberts