1. 5.3 Concurrent Lines, Medians, and Altitudes
Stand Stand 0_
Can you figure out the puzzle below???
No one understands!

2. 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.... 2

3. 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 P k 3

4. Properties of Bisectors
Circumcenter of the Triangle: The point of concurrency of the perpendicular bisectors of a triangle.
Theorem 5-6: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. 4

5. Properties of Bisectors
Incenter of the Triangle: The point of concurrency of the angle bisectors of a triangle.
Theorem 5-7: The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. 5

6. Definitions
Median of a Triangle: A segments whose endpoints are a vertex and the midpoint of the opposite side.
Altitude of a Triangle: Perpendicular segment from a vertex to the line containing the opposite side.

7. 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. 7

8. Properties of Medians
In the figure below, DE = 6 and AD = 16. Find DB and AF. F 8

9. 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. 9

10. Sum It Up which is… Figure concurrent at.. circumcenter
equidistant from vertices
bisector
bisector
incenter
equidistant from sides
median
centroid
2/3 distance from vertices to midpoint
altitude
orthocenter 10

11. 5.3 Concurrent Lines, Medians, and Altitudes
KNEE
LIGHT LIGHT
Can you figure out the puzzle below???
HW 5.3: #8-9, 11-16, 19-22, 28
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