1. Sect. 5.4 Midsegment Theorem
Goal Using Midsegments of Triangles.
Goal Using Properties of Midsegments.

2. Using Midsegments of a Triangle
A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle

3. Theorem 5.9 Midsegment Theorem
Using Midsegments of a Triangle
Theorem 5.9 Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.

4. Show that midsegment is parallel to and is half as long.
Using Midsegments of a Triangle
Show that midsegment is parallel to and is half as long.

5. Using Midsegments of a Triangle
Find JK and AB

6. a) What are the coordinates of Q and R?
Using Midsegments of a Triangle
a) What are the coordinates of Q and R?
b) Why is
c) What is MP? What is QR?

7. a) In XYZ, which segment is parallel to
Using Midsegments of a Triangle
a) In XYZ, which segment is parallel to
b) Is Why?
c) Find YZ and XY

8. Using Midsegments of a Triangle
Given: DE = x + 2; BC =
Find DE

9. Using Properties of Midsegments
The midpoints of the sides of a triangle are S(1, 5), T(3, 3), and V(4, 6). What are the coordinates of the vertices of the triangle?

10. are midsegments in XYZ. Find the perimeter of XYZ.
Using Properties of Midsegments
are midsegments in XYZ. Find the perimeter of XYZ.

11. Find the perimeter of the triangle and the midsegment triangle.
Using Properties of Midsegments
The midpoints of the sides of a triangle are S(1, 5), T(3, 3), and V(4, 6).
Find the perimeter of the triangle and the midsegment triangle.
*The perimeter of a midsegment triangle is half the perimeter of the original triangle.

12. Find the perimeter of  ABC.
Using Properties of Midsegments
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.

13. Homework
, 26-29, 36a-e, even