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Special Segments in Triangles Part 1 March 22, 2015

Lesson 27/28Special Segments in Triangles

***This is different than on your notetaking guide***

Special Segments in Triangles Part 1 March 22, 2015

PART 1 - VOCABULARY

Special Segments in Triangles Part 1 March 22, 2015

PerpendicularBisector

AngleBisector Median Altitude

Circumcenter Incenter Centroid Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A line that is perpendicular to a

segment at its midpoint.

AngleBisector Median Altitude

Circumcenter Incenter Centroid Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A ray that divides an angle into two congruent angles

PerpendicularBisector Median Altitude

Circumcenter Incenter Centroid Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A segment whose endpoints are a vertex of a triangle

and the midpoint of the opposite side.

PerpendicularBisector

AngleBisector Altitude

Circumcenter Incenter Centroid Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A perpendicular segment from a vertex of a triangle to the line containing the

opposite side.

PerpendicularBisector

AngleBisector Median

Circumcenter Incenter Centroid Orthocenter

Obtuse Triangle two of the altitudes are outside the triangle.

Right Triangletwo of the altitudes are legs of the triangle.

Acute TriangleAll of the altitude are inside the triangle

Special Segments in Triangles Part 1 March 22, 2015

Is AB as a median, altitude, angle bisector, or perpendicular bisector?

Special Segments in Triangles Part 1 March 22, 2015

Concurrent the point at which three or more lines intersect.

For any triangle, certain sets of lines are always concurrent.

Special Segments in Triangles Part 1 March 22, 2015

A line that is perpendicular to a

segment at its midpoint.

The point of concurrency of the perpendicular

bisectors.

AngleBisector Median Altitude

Incenter Centroid Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A ray that divides an angle into two congruent angles

The point of concurrency of the angle bisectors.

PerpendicularBisector Median Altitude

Circumcenter Centroid Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A segment whose endpoints are a vertex of a triangle

and the midpoint of the opposite side.

The point of concurrency of the medians.

PerpendicularBisector

AngleBisector Altitude

Circumcenter Incenter Orthocenter

Special Segments in Triangles Part 1 March 22, 2015

A perpendicular segment from a vertex of a triangle to the line containing the

opposite side.

The point of concurrency of the altitudes.

PerpendicularBisector

AngleBisector Median

Circumcenter Incenter Centroid

Special Segments in Triangles Part 1 March 22, 2015

"All of my children

are bringing in

peanut butter cookies."

All of

My children

Are Bringing In

Peanut Butter Cookies

=

=

==

Perpendicular Bisectors, Circumcenter

Angle Bisectors, Incenter

Medians, Centroid

Altitudes, Orthocenter

***Be careful not to mix up centroid and circumcenter***

More Acronyms

Special Segments in Triangles Part 1 March 22, 2015

ExploreAre the points of concurrency always inside the triangle?

Special Segments in Triangles Part 1 March 22, 2015

PerpendicularBisector

AngleBisector Median Altitude

Circumcenter Incenter Centroid Orthocentercan be outside of the triangle

can be outside of the triangle

always inside the triangle

always inside the triangle

Special Segments in Triangles Part 1 March 22, 2015

PRACTICE

Special Segments in Triangles Part 1 March 22, 2015

PR

QT median

altitude

angle bisector

perpendicular bisector

none

Special Segments in Triangles Part 1 March 22, 2015

H

AD

EG

CF

HD

median

altitude

angle bisector

perpendicular bisector

none

Special Segments in Triangles Part 1 March 22, 2015

Classify each red segment as a median, altitude, angle bisector, perpendicular bisector, or neither.

median

altitude

angle bisector

perpendicular bisector

none

Special Segments in Triangles Part 1 March 22, 2015

The point of concurrency of the perpendicular bisectors is the ______.

The point of concurrency of the altitudes is the ________.

The point of concurrency of the medians is the ________.

The point of concurrency of the angle bisectors is the ________.

orthocenter

incenter

circumcenter

centroid

Special Segments in Triangles Part 1 March 22, 2015

Which point is the centroid?

Special Segments in Triangles Part 1 March 22, 2015

Which point is the orthocenter?

Special Segments in Triangles Part 1 March 22, 2015

Homework:*Lesson 26 PRACTICE

*Lesson 27/28 PRACTICE 1

*Study the 8 vocabulary words on the foldableYou may want to use an acronym to help!

Special Segments in Triangles Part 1 March 22, 2015