1. Midsegments of Triangles

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 its length

3. Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

4. Angle Bisector Theorem
If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
Converse of the Angle Bisector Theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.

5. In XYZ, M, N, and P are midpoints. The perimeter of MNP is 60
In XYZ, M, N, and P are midpoints. The perimeter of MNP is 60. Find NP and YZ.

6. Find x, FB, and FD in the diagram above.
FD = FB Angle Bisector Theorem
7x – 37 = 2x Substitute.
7x = 2x Add 37 to each side.
5x = Subtract 2x from each side.
x = Divide each side by 5.
FB = 2(8.4) + 5 = Substitute.
FD = 7(8.4) – 37 = Substitute.

7. Assignment
P 262 #1-12 P 267 #1-4, 6-26