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The greatest mistake you can make in life is to be continually fearing you will make one. -- Elbert Hubbard. Bisectors, Medians, Altitudes. Chapter 5 Section 1 Learning Goal: Understand and Draw the concurrent points of a Triangle. Points of Concurrency.

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Presentation Transcript
bisectors medians altitudes

The greatest mistake you can make in life is to be continually fearing you will make one. -- Elbert Hubbard

Bisectors, Medians, Altitudes

Chapter 5 Section 1

Learning Goal: Understand and Draw the concurrent points of a Triangle

points of concurrency
Points of Concurrency

When three or more lines intersect at a common point, the lines are called Concurrent Lines.

Their point of intersection is called the point of concurrency.

Concurrent Lines

Non-Concurrent Lines

draw the perpendicular bisectors
Draw the Perpendicular Bisectors

Extend the line segments until they intersect

Their point of concurrency is called the circumcenter

Draw a circle with center at the circumcenter and a vertex as the radius of the circle

What do you notice?

draw the angle bisectors
Draw the Angle Bisectors

Extend the line segments until they intersect

Their point of concurrency is called the incenter

Draw a circle with center at the incenter and the distance from the incenter to the side as the radius of the circle

What do you notice?

draw the median of the triangle
Draw the Median of the Triangle

Their point of concurrency is called the centroid

Extend the line segments until they intersect

The Centroid is the point of balance of any triangle

centroid theorem
Centroid Theorem

How does it work?

9

1/3

15

y

2/3

x

draw the altitudes of the triangle
Draw the Altitudes of the Triangle

Their point of concurrency is called the orthocenter

Extend the line segments until they intersect

coordinate geometry
Coordinate Geometry

The vertices of ΔABC are A(–2, 2), B(4, 4), and C(1, –2). Find the coordinates of the orthocenter of ΔABC.

points of concurrency1
Points of Concurrency
  • Questions:
  • Will the P.O.C. always be inside the triangle?
  • If you distort the Triangle, do the Special Segments change?
  • Can you move the special segments by themselves?
  • Hyperlink to Geogebra Figures
  • circumcenter Geogebra\Geog_Circumcenter.ggb
  • incenter Geogebra\Geog_Incenter.ggb
  • centroidGeogebra\Geog_centroid.ggb
  • orthocenterGeogebra\Geog_orthocenter.ggb
homework
Homework
  • Pages 275 – 277; #16, 27, 32 – 35 (all), 38, 42, and 43. (9 problems)
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