Integrated Math 3
Section 5-5
Inequalities for One Triangle
Example: Ordering Triangle Side Lengths
and Angle Measures
Write the angles in order from
smallest to largest.
The shortest side is
smallest angle is F.
The longest side is
, so the
, so the largest angle is G.
The angles from smallest to largest are
F, H and G.
Example: Ordering Triangle Side Lengths
and Angle Measures
Write the sides in order from
shortest to longest.
mR = 180° – (60° + 72°) = 48°
The smallest angle is R, so the
shortest side is
.
The largest angle is Q, so the longest side is
The sides from shortest to longest are
.
Example :
Write the angles in order from
smallest to largest.
The shortest side is
smallest angle is B.
The longest side is
, so the
, so the largest angle is C.
The angles from smallest to largest are B, A, and C.
If you know 2 of the sides you can give a range of what the third side
length is. To get the lowest number the third side could be, subtract
the two sides you know. To get the highest number the third side could
be, add the two sides you know. Write your answer in this form:
# < side < #
Subtract 51 – 46 to get the low number and
add 51 + 46 to get the high number.
5 < x < 97
Example: Applying the
Triangle Inequality Theorem
Tell whether a triangle can have sides with the
given lengths. Explain.
7, 10, 19
No—by the Triangle Inequality Theorem, a triangle
cannot have these side lengths.
Example: Applying the
Triangle Inequality Theorem
Tell whether a triangle can have sides with the
given lengths. Explain.
2.3, 3.1, 4.6


Yes—the sum of each pair of lengths is greater
than the third length.

Lesson Quiz: Part I
1. Write the angles in order from smallest to
largest.
C, B, A
2. Write the sides in order from shortest to
longest.
Lesson Quiz: Part II
3. The lengths of two sides of a triangle are 17 cm
and 12 cm. Find the range of possible lengths for
the third side.
5 cm < x < 29 cm
4. Tell whether a triangle can have sides with
lengths 2.7, 3.5, and 9.8. Explain.
No; 2.7 + 3.5 is not greater than 9.8.
5. Ray wants to place a chair so it is
10 ft from his television set. Can
the other two distances
shown be 8 ft and 6 ft? Explain.
Yes; the sum of any two lengths is
greater than the third length.
Homework
Section 5-5 p.146, #1-17 all