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Midsegments of Triangles
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:
Goals for this section:
Students will learn what a midsegment in a triangle is and the properties attributed to it.
Triangle Midsegment Theorem
Triangle Midsegment Theorem
Midsegment: a segment connecting the midpoints of two sides of a triangle
Midsegment: a segment connecting the midpoints of two sides of a triangle
Theorem
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
Example 1
What is m∠DBC?
What is m∠DBC?
Statements
- AB ≅ BC, ED ≅ DC
- BD is the midsegment of ΔACE
- AE || BD
- m∠DBC = 60
Reasons
- Given
- Definition of midsegment
- Triangle Midsegment Theorem
- Corresponding Angles Postulate
Example 2
Example 2
Name 3 pairs of parallel segments.
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.
External Resources
External Resources
Keywords: midsegments, triangle
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