1. Appetizer
Draw, label, and cut out a large triangle; it does not matter what type of triangle. Label (on the inside), the vertices A, B, and C.
Fold A onto C to find the midpoint of AC. Do the same for BC. Label the midpoints L and N, respectively. Draw LN.
Fold each triangle on LN.
Fold A to C; fold B to C.
Discussion
How does LN compare to AB? Explain.
Make a conjecture about how the segment joining the midpoints of two sides of a triangle is related to the third side of the triangle.

2. Section 5-1: Midsegments of Triangles
Triangle Midsegment Theorem
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. Section 5-2: Bisectors in Triangles
Key Terms
The distance between two objects is the length of the shortest path between them.
Postulate: A line segment is the shortest path between two points.
If two points are the same distance from a third point, then that third point is equidistant from the first two points. A B
Say what? C

4. Key Terms (cont.)
The perpendicular bisector of a segment is the line that bisects and is perpendicular to the segment. C
Say what? A D B

5. Perpendicular Bisector Theorem (PBT)
Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment. X
Say what? A B Y
any point (along the perpendicular bisector)
endpoints

6. Converse of the Perpendicular Bisector Theorem (CPBT)
Theorem: If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment. X
Say what? A B Y
two points
endpoints

7. More Key Terms!
The distance from a point to a line is the length of the perpendicular segment from the point to the line. X A D Y

8. Angle Bisector Theorem (ABT)
Theorem: If a point is on the bisector of an angle, then it is equidistant from the sides of that angle. X B
Say what? A D C Y
any point (along the angle bisector)
sides

9. Converse of the Angle Bisector Theorem (CABT)
Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the angle bisector. X B
Say what? A D C Y
any point
sides
angle bisector