1. 5.5: Midsegments of a Triangle
Objective:
Define midsegment of a triangle.
Use properties of midsegments to solve.

2. What is a Midsegment of a Triangle?
Concept:
What is a Midsegment of a Triangle?
The midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle.
Every triangle has three midsegments.
The midsegment is always half the length of the side that is parallel to it..

3. Definition of Midsegment of a Triangle
Concept:
Definition of Midsegment of a Triangle
The midsegment of a triangle is the segment whose endpoints are the midpoints of two sides of the triangle
Midsegment
Base
Midsegment = ½ of Base
M = ½ b

4. Concept: Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half of its length
Midsegment x 2x

5. Find the length of the midsegment.
Concept:
Midsegment of a Triangle cont…
Find the length of the midsegment.
M = ½ b 23
M = ½ • 46 46
M = 23

6. Find the length of the base.
Concept:
Midsegment of a Triangle cont…
Find the length of the base.
M = ½ b 46 2•
46= ½ b 2• 92
92 = b

7. Find the length of the midsegment and the base.
Concept:
Midsegment of a Triangle cont…
Find the length of the midsegment and the base.
M = ½ b
5x - 1 = ½(6x + 10)
5•3-1
= 14
5x - 1 = 3x + 5
-3x x
5x - 1
2x - 1 = 5
+1 +1
6x + 10
2x = 6
6•3+10
= 28
x = 3