Download 5.5 Inequalities In One Triangle

yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Golden ratio wikipedia, lookup

Noether's theorem wikipedia, lookup

Perceived visual angle wikipedia, lookup

Reuleaux triangle wikipedia, lookup

History of trigonometry wikipedia, lookup

Euclidean geometry wikipedia, lookup

Rational trigonometry wikipedia, lookup

Trigonometric functions wikipedia, lookup

Incircle and excircles of a triangle wikipedia, lookup

Integer triangle wikipedia, lookup

Pythagorean theorem wikipedia, lookup

5.5 Inequalities In One
Essential Question:
How do you determine the
largest/smallest sides and angles in a
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.
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
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
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.
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.
10 cm, 14 cm
8 ft, 17 ft
a units, b units
Example: Determine the possible
values of x