Transcript Triangle Inequalities

Triangle Inequalities
Objectives:
1. Discover inequalities among
sides and angles in triangles.
Triangle Inequality Conj.
The sum of the lengths of the
shorter two sides of a triangle
than the length of
is greater
___________
the third side.
Is it possible to have a
triangle with the following
side measures?
Is it possible to have a
triangle with the following
side measures?
Is it possible to have a
triangle with the following
side measures?
Is it possible to have a
triangle with the following
side measures?
Side-Angle Inequality Conj
In a triangle,
the longest side is opposite the angle
with greatest measure, and
the shortest side is opposite the
angle with the least measure.
List the sides in order from
shortest to longest.
List the angles in order from
smallest to greatest measure.
Definitions:
If you extend
one side of a
triangle from the
vertex, you form
an exterior
angle.
exterior angle
The angle
adjacent to the
exterior angle.
adjacent interior angle
The two angles
that are nonadjacent to the
exterior angle.
remote interior angles
Triangle Exterior Angle
Conjecture:
The measure of an exterior angle of
a triangle is equal to the sum of the
measures of the remote interior
angles.
What does Triangle Exterior
angle Conjecture mean?
mA = mB + mC
mA= ?
mA=120°
mB= ?
mB=138°
mC= ?
mC=83°