Warm up: Solve for x.
Linear Pair
4x + 3
7x + 12
X = 15
Special
Segments in
Triangles
Median
Altitude
Tell whether each red segment is an altitude
of the triangle.
The altitude is
the “true height”
of the triangle.
Perpendicular Bisector
Tell whether each red segment is an
perpendicular bisector of the triangle.
Angle Bisector
Start to memorize…
•Indicate the special
triangle segment based
on its description
I cut an angle into two
equal parts
I connect the vertex to
the opposite side’s
midpoint
I connect the vertex to
the opposite side and I’m
perpendicular
I go through a side’s
midpoint and I am
perpendicular
Drill & Practice
•Indicate which special
triangle segment the
red line is based on the
picture and markings
Multiple Choice
Identify the red segment
Q1:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q2:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q3:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q4:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q5:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q6:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q7:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Multiple Choice
Identify the red segment
Q8:
A. Angle Bisector
C. Median
B. Altitude
D. Perpendicular Bisector
Points of
Concurrency
New Vocabulary
(Points of Intersection)
1.
2.
3.
4.
Centroid
Orthocenter
Incenter
Circumcenter
Point of Intersection
intersect at the
Important Info about the Centroid
• The intersection of the medians.
• Found when you draw a segment from one
vertex of the triangle to the midpoint of the
opposite side.
• The center is two-thirds of the distance from
each vertex to the midpoint of the opposite
side.
• Centroid always lies inside the triangle.
• This is the point of balance for the triangle.
The intersection of
the medians is
called the
CENTROID.
Point of Intersection
intersect at the
Important Info about the Orthocenter
• This is the intersection point of the altitudes.
• You find this by drawing the altitudes which is
created by a vertex connected to the opposite
side so that it is perpendicular to that side.
• Orthocenter can lie inside (acute), on (right),
or outside (obtuse) of a triangle.
The intersection
of the altitudes is
called the
ORTHOCENTER.
Point of Intersection
intersect at the
Important Info about the Incenter
• The angle bisectors of a triangle intersect at a
point that is equidistant from the sides of the
triangle.
• Incenter is equidistant from the sides of the
triangle.
• The center of the triangle’s inscribed circle.
• Incenter always lies inside the triangle
The intersection
of the angle
bisectors is called
the INCENTER.
Point of Intersection
intersect at the
Important Information about the
Circumcenter
• The perpendicular bisectors of a triangle
intersect at a point that is equidistant from
the vertices of the triangle.
• The circumcenter is the center of a circle that
surrounds the triangle touching each vertex.
• Can lie inside an acute triangle, on a right
triangle, or outside an obtuse triangle.
The intersection of
the perpendicular
bisector is called
the
CIRCUMCENTER.
Memorize these!
MC Medians/Centroid
AO Altitudes/Orthocenter
ABI Angle Bisectors/Incenter
PBCC Perpendicular Bisectors/Circumcenter
Will this work?
MC
Ate
Our
AO
ABI Avocados But I
PBCC Prefer Burritos Covered in Cheese
My Cousin