Download Geometry B Date: ______ 5.5-5.6 Triangle Inequality in One and

Geometry B
Date: _____________
5.5-5.6 Triangle Inequality in One and Two Triangles
Objective: To apply triangle inequalities in one and two triangles
Key Concepts:
 The longest side in a triangle is across from the ___________________ angle.

The shortest side in a triangle is across from the __________________ angle.
Ex. 1: Ordering Triangle Side Lengths and Angle Measures
Write the sides and angles in order from smallest to largest.
a.
b.
Sides: _______, _________, ________
Angles: _______, _________, ________
Angles: _______, _________, ________
Sides: _______, _________, ________
Triangle Inequality

A triangle is made of 3 segments, but not every set of 3 segments can form a triangle.

The sum of the two smallest sides must be __________________________________

If this is not true, then ___________________________________________________
To Test: Add the two smallest sides.
Ex. 1: State whether it is possible to form a triangle with the given side lengths.
a. 3 in, 3 in, 8 in
b. 7 in, 4 in, 4 in
c. 6 in, 6 in, 12 in
d. 9 in, 5 in, 11 in
Ex. 2: Find the possible lengths of the 3rd side of the triangle described below.
a. A triangle has one side of 10 cm and another of 14 cm.
Option 1: 14 is the largest side.
Find the smallest side (Subtract 14 – 10)
Option 2: 10 and 14 are the smaller sides.
Find the largest side (add 14 +10)
Answer: The 3rd side could be between _____ and ____ cm long.
b. A triangle has one side of 8 cm and another of 17 cm.
Option 1:
Option 2:
Answer:
Hinge Theorem: If two triangles have 2 pairs of congruent sides but the included angles are not
congruent, then the longer 3rd side will be across from the _________________________________.
Compare the measures of BAC and DAC.
Find the range of values for the variable k.
Compare the lengths of sides EF and FG.
Find the range of values for the variable z.
HW: 5.5-5.6 Worksheet