Thinking Page…

Directions: Take out your math encyclopedia and review your notes for this unit. Write two paragraphs using complete sentences and correct grammar to reflect on the following writing prompts.

Reflection #1: What is the most significant thing you learned this week?

Reflection #2:What questions are still unanswered at the end of this week?

5.3 Concurrent Lines, Medians, and Altitudes

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Learning Target…

To identify properties of perpendicular bisectors and angle bisectors, medians, and altitudes.

Purpose: To be able to find locations in a park to place a fountain, statue, playground, etc....

Definitions

Concurrent Lines: Three or more lines that meet at one point.

Point of Concurrency: The point at which concurrent lines meet.

l

m

n

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k

Properties of Bisectors

Theorem 5-6: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.

Circumcenter of the Triangle: The point of concurrency of the perpendicular bisectors of a triangle.

Properties of Bisectors

Theorem 5-7: The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides.

Incenter of the Triangle: The point of concurrency of the angle bisectors of a triangle.

Definitions

Altitude of a Triangle: Perpendicular segment from a vertex to the line containing the opposite side.

Median of a Triangle: A segments whose endpoints are a vertex and the midpoint of the opposite side.

Properties of Medians

Centroid of a Triangle: The point of concurrency of the medians of a triangle.

Theorem 5-8: The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite sides.

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Properties of Medians

In the figure below, DE = 6 and AD = 16. Find DB and AF.

F

Properties of Altitudes

Orthocenter of a Triangle: The point of concurrency of the lines containing the altitudes of a triangle.

Theorem 5-9: The lines that contain the altitudes of a triangle are concurrent.

Sum It Up

Figure concurrent at.. which is…

bisector circumcenter

incenter

centroid

orthocenter

median

bisector

altitude

equidistant from vertices

equidistant from sides

2/3 distance from vertices to midpoint

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5.3 Concurrent Lines, Medians, and Altitudes

HW 5.3: #8-9, 11-16, 19-22, 28

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