1. Basics
2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

 

Medians, Altitudes, and Perpendicular Bisectors

 

Objective:

            •    Understanding about the properties of medians, altitudes, and perpendicular ( |_) bisectors.

 

Lesson 4-3 Medians, Altitudes, and Perpendicular Bisectors

            Median: A segment from a vertex to the midpoint of the opposite side

            Altitude: The perpendicular segment from a vertex to the line that contains the opposite side.

In an acute triangle all of the altitudes are all inside the triangle.

 

 

In a right triangle, two of the altitudes are the legs of the triangle and the third is inside the triangle.

 

 

In an obtuse triangle, two of the altitudes are outside of the triangle.

 

 

      Perpendicular Bisector: a line (or ray or segment) that is perpendicular to the segment at its midpoint.

 

Theorem 4-5 If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment. Segment AB is Segment BC by Theorem 4-5   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.   Theorem 4-7 If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.   Theorem 4-8 If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

 

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