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Bisectors, Medians, Altitudes

- The greatest mistake you can make in life is to

be continually fearing you will make one. --

Elbert Hubbard

- Chapter 5 Section 1
- Learning Goal Understand and Draw the concurrent

points of a Triangle

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

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

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

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 is the point of balance

Centroid Theorem

How does it work?

9

1/3

15

y

2/3

x

Centroid Theorem

Draw the Altitudes of the Triangle

Their point of concurrency is called the

orthocenter

Extend the line segments until they intersect

Coordinate Geometry

The vertices of ?ABC are A(2, 2), B(4, 4), and

C(1, 2). Find the coordinates of the orthocenter

of ?ABC.

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

- Pages 275 277 16, 27, 32 35 (all), 38, 42,

and 43. (9 problems)

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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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