5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

Lesson 5.3 Medians, Altitudes, Angle Bisector & Perpendicular Bisectors

1 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

VOCABULARY In a triangle, an angle bisector is a segment from the VERTEX of the angle to its opposite side on the ray______the angle.

is an angle bisector of ∆ABD from vertex A to side

Angle Bisector

2 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

A median of a triangle is a segment drawn from a VERTEX to the MIDPOINT of the opposite side.

is a median of ∆FGH from vertex F to side .

3 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

An altitude of a triangle is a perpendicular segment drawn from a VERTEX to the line that contains the OPPOSITE side. An altitude may lie outside of the triangle. It may also be a side of the triangle.

In these two triangles, is an altitude of In ∆PRQ, is the ∆KLM from vertex L. altitude from P and is the altitude from R.

4 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

A perpendicular bisector of a side of a triangle is a line perpendicular to a side through the MIDPOINT of the side. A perpendicular bisector of in ∆ABC is shown.

5 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

Examples

Given obtuse triangle ∆AGD with obtuse angle ∠G, and . Identify a median, an angle bisector, an altitude and a perpendicular bisector. 1. Name an angle bisector. ______

2. Name a median. ______

3. Name a perpendicular bisector. ______

4. Name an altitude. ______

6 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

Practice

Use the figure to the right.

1. Name an angle bisector. ______

2. Name a median. ______3. Name a perpendicular bisector. ______

4. Name an altitude. ______

7 5.3 Medians, Altitudes, Angle and Perpendicular Bisectors (5.1­5.2).notebookDecember 04, 2013

PERPENDICULAR BISECTOR THEOREM A point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment.

C F CP is the perpendicular E bisector of AB A P B

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