Transcript Triangle Inequalities

5.5 Triangle Inequalities, Thompson
Objectives
1.
2.
3.
4.
To complete and use the Triangle Inequality
Matching shortest to longest…
Can you make a triangle…
Possible range of third side
Making Triangles, YAY!
Given three segments of any length, can you construct
a triangle?
Investigation 1
So this is what happens
when two sides of a
“triangle” together are
smaller than the third
side:
And here’s what happens
with two sides of a
“triangle” together are
equal to the third side:
Definition of Inequality
For any real numbers a and b, a > b if and only if there
is a positive number c such that a = b + c.
Thus:
 10 > 6 because 10 = 6 + 4
 If m1 + m2 = m3, then m1 < m3.

> versus
≥
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
Example
Determine whether it is possible to draw a triangle
with sides of the given measures.
1.
2.
3.
1 cm, 2 cm, 3 cm
21 in, 32 in, 18 in
11 m, 6 m, 2 m
Look at range of possible third sides here…
Example
The two measures of two sides of a triangle are given.
Between what two numbers must the measure of
the third side fall? Write your answer as a
compound inequality.
1. 21 and 27
2. 5 and 11
3. 30 and 30
Investigation 2
Use the following Investigation to discover the
relationship between the measures of angles in
triangles and the lengths of the sides opposite
them.
Investigation 2
1.
2.
Draw a large scalene
triangle. Guys draw
acute triangles, and the
Gals should draw
obtuse triangles.
Measure the angles in
each triangle. Label the
angle with greatest
measure L, the angle
with second greatest
measure M, and the
remaining angle S.
Investigation 2
3.
Measure the three sides. Which side is the
longest? Label it by placing the lowercase letter l
near the middle of the side. Which side is the
second longest? Label it m in the same way.
Which side is the shortest? Label it s.
Investigation 2
Which side, l, m, or s, is
opposite the angle with
the greatest measure?
Which side is opposite
the angle with the least
measure?
Investigation 2
Which side, l, m, or s, is
opposite the angle with
the greatest measure?
Which side is opposite
the angle with the least
measure?
Example 7
In the triangle at the
right, put the unknown
measures in order from
greatest to least.
55
b
c
68
a
Classwork
 Page 260 14 - 22
 Page 277
5
– 27 odd 32, 34-36
 Page 155
 25, 54
 Page 162
 13, 15, 21
 Page 284
 Chapter Test (skip 1-6, 15)