Download 5.5 Inequalities In One Triangle

5.5 Inequalities In One
Triangle
Essential Question:
How do you determine the
largest/smallest sides and angles in a
triangle?
Theorem

If one side of a triangle is longer than
another side, then the angle opposite the
longer side is larger than the angle
opposite the shorter side.
Theorem

If one angle of a triangle is larger than
another angle, then the side opposite the
larger angle is longer than the side
opposite the smaller angle.
Example: Write the measures in the
triangle in order from least to
greatest.
Exterior Angle Inequality Theorem

The measure of an exterior angle of a
triangle is greater than the measure of
either of the two nonadjacent interior
angles.
Triangle Inequality Theorem


The sum of the lengths of any two sides
of a triangle is greater than the length of
the third side.
This theorem is used to determine if a
triangle can be formed from a given set of
side lengths (the sum of the smaller sides
must be greater than the larger side).
Example: Determine if it is possible
to construct a triangle with the
given side lengths.
1.
2.
3.
4.
3
3
9
2
cm, 4cm, 5cm
in, 3in, 8in
ft, 5 ft, 11 ft
cm, 2cm, 2cm
Determining the length of the third
side of a triangle



If you know two side lengths of a triangle,
you may determine the possible lengths of
the third side:
______ < x < _______
To find the value of the first blank:
subtract the given values
To find the value of the second blank:
add the given values
Example: Two of a triangle’s side
lengths are given. Describe the
possible lengths of the third side.
1.
2.
3.
10 cm, 14 cm
8 ft, 17 ft
a units, b units
Example: Determine the possible
values of x