1. 5-4 The Triangle midsegment theorem
Chapter5
5-4 The Triangle midsegment theorem

2. objectives
Prove and use properties of triangle midsegments.

3. Midsegment of a triangle
A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

4. Example 1: Examining Midsegments in the Coordinate Plane
The vertices of ∆XYZ are X(–1, 8), Y(9, 2), and Z(3, –4). M and N are the midpoints of XZ and YZ. Show that and
Step 1 Find the coordinates of M and N.

5. solution Step 2 Compare the slopes of MN and XY.
Since the slopes are the same, they are parallel

6. solution
Step 3 Compare the heights of MN and XY.

7. Example#2
The vertices of ΔRST are R(–7, 0), S(–3, 6), and T(9, 2). M is the midpoint of RT, and N is the midpoint of ST. Show that and

8. Midsegment theorem
The relationship shown in Example 1 is true for the three midsegments of every triangle.

9. Example#3
Find each measure. BD
Solution:
BD = 8.5

10. Example#4
Find each measure.
mCBD
mCBD = mBDF
mCBD = 26°

11. Example #5
In an A-frame support, the distance PQ is 46 inches. What is the length of the support ST if S and T are at the midpoints of the sides?
ST = 23

12. Student guided practice
Do problems 2-6 in your book page 336

13. Homework
Do problems10-16 in your book page 336