Download Inequalities In One Triangle

Inequalities In One
Triangle
Chapter 5 Section 6
Objective
Students will use inequalities involving
angles and sides of triangles.
Angles and Sides
Angles and sides of a triangle have special
relationships that involve inequalities.
Comparison Property of Inequality
If a = b + c and c > 0, then a > b
Note: a, b, and c are sides of a triangle.
Corollary to the Triangle Exterior
Angle Theorem
The measure of an exterior angle of a
triangle is greater than the measure of
each of its remote interior angles.
On page 325…
Look at Problem 1
Try the “Got It” problem for Problem 1.
Theorem 5-10
If two sides of a triangle are not congruent,
then the larger angle lies opposite the
longer side.
Theorem 5-11
If two angles of a triangle are not
congruent, then the longer side lies
opposite the larger angle.
Theorem 5-12
The sum of the lengths of any two sides of
a triangle is greater than the length of the
third side
Y
XY + YZ > XZ
YZ + XZ > XY
XZ + XY >YZ
X
Z
Turn to page 327…
Look at Problem 4 at the bottom of the
page
Try the “Got It” problem #4
On page 328…
Try problems #1-8 on your own.
In small work groups…
Complete problems #9-32 on page 329.
Exit Slip
1. Given only 3 measurements, how can
you determine if the shape is a triangle?
2. Given three angle measures, how can
you determine which side is the
shortest? The longest?