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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