Chapter 6

More About
a segment in a triangle
that joins a vertex of the
triangle and the midpoint
of the side opposite that
medians of a triangle
intersect at a common point
called the centroid.
When three or more lines
or segments meet at the
same point, they are
 The
length of the
segment from the vertex
to the centroid is twice
the length of the segment
from the centroid to the
Altitudes and
Perpendicular Bisectors
A perpendicular
segment in which one
endpoint is at a vertex
and the other endpoint is
on the side opposite that
A segment or line that
contains the midpoint of
the side of a triangle and
is perpendicular to that
Angle Bisectors of
ray whose endpoint is
the vertex and is located
in the interior of the angle
that separates a given
angle into two angles with
equal measure
Isosceles Triangles
two sides of a triangle
are congruent, then the
angles opposite those
sides are congruent.
 The
median from the
vertex angle of an
isosceles triangle lies on
the perpendicular bisector
of the base and the angle
bisector of the vertex
If two angles of a triangle
are congruent, then the
sides opposite those angles
are congruent.
Right Triangles
The side opposite the
right angle
 The
two sides that form
the right angle
If two legs of one right
triangle are congruent to
the corresponding legs of
another right triangle
then the triangles are
The Pythagorean
In a right triangle, the
square of the length of the
hypotenuse c is equal to
the sum of the squares of
the lengths of the legs a
and b.
Distance on the
Coordinate Plane
d is the distance
between two points
(x1, y1) and (x2, y2), then
d = (x2 – x1 + (y2 – y1