Chapter 6

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More About
Triangles
Medians
Is
a segment in a triangle
that joins a vertex of the
triangle and the midpoint
of the side opposite that
vertex
The
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
concurrent.
 The
length of the
segment from the vertex
to the centroid is twice
the length of the segment
from the centroid to the
midpoint.
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
vertex.

A segment or line that
contains the midpoint of
the side of a triangle and
is perpendicular to that
side.

Angle Bisectors of
Triangles
A
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
If
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
angle.

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
congruent.

The Pythagorean
Theorem
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
If
d is the distance
between two points
(x1, y1) and (x2, y2), then
d = (x2 – x1 + (y2 – y1
2
)
2
)

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