Warm up

1
Warm up

• Draw the following types of triangles and mark
  them correctly.
• Isosceles
• Equilateral
• Scalene
• Right
• Obtuse

2

Triangle Centers

• What are they?
• Where are they?
• How are they found?

3
Triangle Centers Points of Concurrency

• What is this all about?
• A Point of Concurrency is a point of
  intersection of 2 or more lines.
• The lines that form a point concurrency are
  called concurrent lines.

4
Median

• The median of a triangle is a segment that
  connects the vertex of a triangle to the midpoint
  of the opposite side. Every triangle has three
  medians.

5
Perpendicular Bisector
6
Altitude

• The altitude of a triangle is a segment that is
  perpendicular to a side of a triangle, and it
  intersects with the vertex opposite that side.

7
Angle Bisector

• The angle bisector is a segment of a triangle
  that bisects an angle of the triangle and then
  intersects the opposite side of the triangle.

8
The Points are

• Incenter
• Circumcenter
• Orthocenter
• Centroid
• Though there are many other points of
  concurrency, which we will see later, we will
  concentrate on these four today.

9
Incenter

• Point of concurrency formed by the intersection
  of the three bisectors of a triangle

Incenter
10
CIRCUMCENTER

• Point of concurrency formed by the intersection
  of three perpendicular bisectors of the sides of
  a triangle

Circumcenter
11
ORTHOCENTER

• Point of concurrency formed by the intersection
  of the three altitudes of a triangle

Orthocenter
12
Centroid

• Point of concurrency formed by the intersection
  of the three medians of a triangle

Centroid
13
The Points are
angle bisectors

• Incenter
• Circumcenter
• Orthocenter
• Centroid

perpendicular bisectors
altitudes
medians
14
Mnemonic Device for points of Concurrency

• PuBliC- Perpendicular Bisectors Circumcenter
• CEMent- Centroid Medians
• ALTo- Altitudes Orthocenter
• BAsIn- Angle Bisector Incenter