1. 5-4 The Triangle Midsegment Theorem Warm Up Lesson Presentation
Lesson Quiz
Holt Geometry

2. Do Now

3. Objective
TSW prove and use properties of triangle midsegments.

4. Vocabulary
midsegment of a triangle

5. 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.

6. 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.
Step 2 Compare the slopes of MN and XY.
Step 3 Compare the heights of MN and XY.

8. 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
Step 1 Find the coordinates of M and N.

10. The relationship shown in Example 1 and 2 is true for the three midsegments of every triangle.

11. Example 3: Using the Triangle Midsegment Theorem
Find each measure. BD CA
mCBD

12. Example 4
Find each measure. JL MP
mMLK

13. Example 5: Indirect Measurement Application
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?

14. Example 6: Indirect Measurement Application
Anna wants to find the distance across the base of Capulin Volcano, an extinct volcano in New Mexico. She measures a triangle at one side of the volcano as shown in the diagram. What is AE?

15. Example 7
What if…? Suppose Anna’s result in Example 4 is correct. To check it, she measures a second triangle. How many meters will she measure between H and F?

16. Example 8: Using the Triangle Midsegment Theorem
Find each measure. UW
mSVU

17. Example 9: Using the Triangle Midsegment Theorem
Find the value of n in each triangle.