1. Lesson 5.3 Lesson 5.3 Midsegment Theorem
Honors Geometry
Lesson 5.3
Midsegment Theorem

2. What You Should Learn Why You Should Learn It
Goal 1: How to identify and construct the midsegments of a triangle
Goal 2: How to use properties of midsegments to solve real-life problems
You can use the midsegments of a triangle to answer questions about triangles that occur in real-life situations such as building a roof framework

3. Midsegment
The midsegment of a triangle is a segment that connects the midpoints of two sides of the triangle

4. Lesson Investigation

5. Observations about midsegments
Midsegment is half the length of the side it is parallel to
Midsegment is parallel to the third side of the triangle

6. Theorem 5.6 Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length

7. Example 1 Illustrating the Midsegment Theorem
Show that the midsegment MN is parallel to the side JK and half its length

8. Example 1 Solution Illustrating the Midsegment Theorem
Begin by using the Midpoint Formula

9. Example 1 Solution Illustrating the Midsegment Theorem
Now find the slopes of JK and MN
(5,2)
(2,1)
Because JK and MN have the same slope, they must be parallel

10. Example 1 Solution Illustrating the Midsegment Theorem
Now use the distance formula to find the lengths JK and MN
(5,2)
(2,1)

11. Using the Midsegment Theorem to draw a triangle
Suppose you are given the three midpoints of the sides of a triangle. Using only these three points, is it possible to construct the original triangle?

12. Example 2 Using Midpoints to draw a triangle
The midpoints of the sides of a triangle are L(4,2), M(2,3) and N(5,4). What are the coordinates of the vertices of the triangle?
Hint: find the slopes of each midsegment

13. Example 2 Using Midpoints to draw a triangle
The midpoints of the sides of a triangle are L(4,2), M(2,3) and N(5,4). What are the coordinates of the vertices of the triangle?
Example 2 Using Midpoints to draw a triangle
Draw a line through M that has a slope of 2
Draw a line through L that has a slope of ⅓
Draw a line through N that has a slope of -½

14. Solution to Example 2
(3,5)
(7,3)
(1,1)

15. THE END