1. Medians, Altitudes, & Perpendicular Bisectors
4-7
Medians, Altitudes, & Perpendicular Bisectors

2. B
Median A C
a segment from a vertex of a triangle to the midpoint of the opposite side of the triangle
Every triangle has 3 medians.
The medians are always on the inside of the triangle.

3. B
Altitude
the perpendicular segment from a vertex of a triangle to the line containing the opposite side of the triangle
Every triangle has 3 altitudes.
The altitudes of a triangle can be inside, outside, or part of the triangle. A C

4. Altitude Locations
Acute
Obtuse
Right
Inside
Outside
On triangle

5. Perpendicular Bisector
Perpendicular Bisector B A C
a line, ray, or segment that is perpendicular to a segment at its midpoint
Every triangle has 3 perpendicular bisectors.

6. Angle Bisector B A C
the ray that divides an angle into two congruent adjacent angles
Every triangle has 3 angle bisectors.

7. Theorem 4 – 5:
A point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment being bisected.

8. Theorem 4 – 6:
If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

9. Theorem 4 – 7:
A point on the bisector of an angle is equidistant from the sides of the angle.

10. Theorem 4 – 8:
If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

11. A X P Z B
Statements
Reasons Y C

12. Section 4.7 Written Exercises (p. 156-157) #7-14, 17, 18, & 20-22
Homework
Section 4.7 Written Exercises (p )
#7-14, 17, 18, & 20-22
Section 4.4 Written Exercises (p ) #17, 18, 22-25, & 27-29