Thinking Page… Directions: Take out your math encyclopedia and review your notes for this unit....
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Transcript of Thinking Page… Directions: Take out your math encyclopedia and review your notes for this unit....
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
Stand Stand0_23456789
Can you figure out the puzzle below???
No one understands!
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
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P
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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2
3
2
3
2
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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