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Geometry
5.5 – Use Inequalities in a Triangle
Learning Target: By the end of today’s lesson we will successfully be able to find possible side lengths of a triangle.
1)
Mark the largest angle, longest side, smallest angle, and shortest side of the triangle shown below.
What do you notice?
The longest side and largest angle are _________________ each other.
The shortest side and smallest angle are __________________ each other.
2) List the sides of ∆PQR in order from shortest to longest.
THEOREM
If one side of a triangle is longer than another side, then the angle opposite
the longer side is _______________ than the angle opposite the shorter side.
AB > BC, So m  ____ > m  _____.
THEOREM
If one angle of a triangle is larger than another angle, then the side opposite
the larger angle is ______________ than the side opposite the smaller angle.
m  A > m  C, So ______ >_______.
3) A long-tailed boat leaves a dock and travels 2500 feet to a cave, 5000 feet to a beach, then 6000 feet back to the
dock as shown below. One of the angles in the path is about 55° and one is about 24°. What is the angle measure of
the path made at the cave?
TRIANGLE INEQUALITY THEOREM
The sum of the lengths of any two sides of a triangle is greater than the
length of the third side.
1) _______+ ______ > AC
2) AC + _____ > ______
3) ______ + AC > ______
*** SHORTCUT*** If given 3 lengths and trying to determine if they could be a triangle, the SUM of the 2 SMALLEST
sides must be GREATER than the third side.
Determine if the following sets of numbers can be a triangle. Justify your answers!
4) 5, 8, 4
5) 16, 12, 28
6) 3, 4, 9
7) 11, 5, 8
*** If trying to find the possible length of a missing side of a triangle ***
(difference of 2 given sides) < missing side < (sum of 2 given sides)
8) A triangle has one side of length 14 and another of
length 10. Describe the possible lengths of the third
side.
9) A triangle has one side of 23 meters and another of
17 meters. Describe the possible lengths of the third
side.