Download 5.5 Inequalities in one triangle

Notes 5-5: Inequalities in One Triangle
Objectives:
Geometry - Ch. 5: Properties and Attributes of Triangles
Apply inequalities in one triangle.
Angle & Side Relationships in Triangles: in a triangle, the largest side is opposite the ____________________ angle.

Similarly, the smallest side is opposite the ____________________ angle.

The ____________________ of each of these is also true.
EX 1: Write the angles in order from smallest to largest.
a) ______ < ______ < ______
(a)
(b)
(a)
(b)
b) ______ < ______ < ______
EX 2: Write the sides in order from smallest to largest.
a) ______ < ______ < ______
b) ______ < ______ < ______
Investigate: Will the following lengths create a triangle?
3
7
4
4
4
7
7
Triangle Inequality Theorem: in a triangle, the sum of any two sides is ____________________ than the third.

______ + ______ > ______

______ + ______ > ______

______ + ______ > ______
 Trick: if 3 lengths can create a triangle, the __________ of the 2 smaller sides should be ________ than the 3rd.
EX 3: Can the following set of side lengths create a triangle?
a) 7, 10, 19
b) 2.3, 3.1, 4.6
________
________
EX 4: The lengths of two sides of a triangle are 17 & 22
inches. Find the range of possible lengths for the third
side.
_____ < x < _____
c) t - 2 , 4t , t2 + 1 when t =4
________
EX 5: Find the possible range of distances between San
Francisco and Oakland.
_____ < x < ____