Transcript Document 7156538

Objectives
• To define, draw, and list characteristics of:
– Midsegments
– Altitudes
– Perpendicular Bisectors
– Medians
1
Medians of Triangles
• A median of a triangle is a segment whose
endpoints are a vertex and the midpoint of
the opposite side.
2
Perpendicular Bisector
• A perpendicular bisector passes through
the midpoint of a segment at a right angle
with that segment
3
Altitude of a Triangle
An altitude is the perpendicular segment
from a vertex to the line containing the
opposite side.
4
Angle Bisector
• An angle bisector connects a vertex to the
opposite side and cuts the vertex angle
into two halves.
5
Midsegments of Triangles
• A midsegment of a triangle is a segment
connecting the midpoints of two sides
6
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides
of a triangle, then the segment is parallel to
the third side, and is half its length.
7
Point of Concurrency Definition
• When three or more lines intersect in one
point, they are concurrent. The point at
which they intersect is the point of
concurrency.
8
Centroid
The point of concurrency of the medians of a
triangle is the centroid. The centroid is also
called the center of gravity because it is the point
where a triangular shape will balance.
The centroid of a triangle is always located inside
the triangle.
9
Circumcenter (Perpendicular Bisectors)
The point of concurrency of the
perpendicular bisectors of a triangle is the
circumcenter of the triangle. The
circumcenter is the center of the circle
which passes around the outside of the
triangle and through each vertex.
10
Orthocenter (Altitudes)
The point of concurrency of the
altitudes of a triangle is the
orthocenter of the triangle.
The orthocenter is inside the
triangle for an acute triangle, at
the right angle for a right
triangle, and outside the
triangle for an obtuse triangle.
11
Incenter (Angle Bisectors)
The point of concurrency of the angle
bisectors of a triangle is the incenter of the
triangle. The incenter is the center of the
circle which lies inside the triangle and
touches all three sides of the triangle. The
incenter is always inside the triangle.
12
For Exploration
http://www.keymath.com/x19398.xml
http://www.keymath.com/x23078.xml
13