Midsegments of Triangles

Standard

G.CO.10 Prove theorems about triangles... the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length.

Goals for this section:

Students will learn what a midsegment in a triangle is and the properties attributed to it.

Triangle Midsegment Theorem

Midsegment: a segment connecting the midpoints of two sides of a triangle

Theorem

If B is the midpoint of AC and D is the midpoint of CE, then

  • BD || AE
  • BD = (1/2)AE
    • This means the segment BD is half the length of AE

Example 1

What is m∠DBC?

Statements

  1. AB ≅ BC, ED ≅ DC
  2. BD is the midsegment of ΔACE
  3. AE || BD
  4. m∠DBC = 60


Reasons

  1. Given
  2. Definition of midsegment
  3. Triangle Midsegment Theorem
  4. Corresponding Angles Postulate

Example 2

Name 3 pairs of parallel segments.

KG is a midsegment by definition. Therefore KG || JH.

GI is a midsegment by definition. Therefore GI || FJ.

IK is a midsegment by definition. Therefore IK || FH.

Keywords: midsegments, triangle