1. The Midsegment Theorem
Goal Using Midsegments of Triangles.
Goal Using Properties of Midsegments.

2. 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 as long.

3. a) In XYZ, which segment is parallel to
Using Midsegments of a Triangle
a) In XYZ, which segment is parallel to
b) Find YZ and XY

4. Quick Check:
Find the m<VUZ. X
65O U Z Y V

5. Identifying Parallel Segments
Example 1
Identifying Parallel Segments
What are the three pairs of parallel segments in triangle DEF?
RS || ____
ST || ____
TR || ____

6. Example 2
In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU.
5 ft
16 ft
TU = ________
PR = ________

7. Example 3
In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY.
14 cm
53 cm
ZY = ________
MN = ________

8. Example 4 Finding Lengths In triangle QRS, T, U, and B are midpoints.
What are the lengths of TU, UB, and QR?

9. Example 5 Find JK and AB 12 JK = ________ 5 AB = ________
Using Midsegments of a Triangle
Find JK and AB 12
JK = ________ 5
AB = ________

10. Example 6
In the diagram, ED and DF are midsegments of triangle ABC. Find the value of x and DF.
3x- 4 52
x = ________ 10
DF = ________ 26

11. Example 7
Given: DE = x + 2; BC =
Find the value of x and DE.
x + 2

12. Example 7
are midsegments in XYZ. Find the perimeter of XYZ.

13. Example 8
Given: X, Y, and Z are the midpoints of AB, BC, and AC respectively. AX = 2; XY = 3; BC = 9
Find the perimeter of  ABC. (it’s a decimal)

14. 5-1 Daily Quiz 12/1 In XYZ, M, N and P are the midpoints.
The Perimeter of MNP is 64.
a) Find NP.
b) Find perimeter of XYZ
a) NP + MN + MP = 64 (Definition of Perimeter)
NP = 64 NP + = 64
NP =
b) P = XY + YZ + ZX
P = ___ + ___ + ____
P = ______ x 24 M P 22 Y Z N