Geometry
5.5 Triangle Inequalities
Name: _______________________
Consider the triangle to the right:
What side is opposite <A: ________________
What side is opposite <B: ________________
What side is opposite <C: ________________
̅̅̅̅ : _______________
What angle is opposite 𝐴𝐵
̅̅̅̅ : _______________
What angle is opposite 𝐵𝐶
What angle is opposite ̅̅̅̅
𝐴𝐶 : _______________
Theorem 5.10: If one side of a triangle is
Theorem 5.11: If one angle of a triangle is
longer than another side, then the angle
larger than another angle, then the side
_________________ the longer side is larger
opposite of the ________________ angle is longer
than the angle opposite the shorter side.
than the side opposite the __________________
angle.
Write the angles from smallest to largest:
Write the sides from longest to shortest:
Write the angles from smallest to largest:
Write the sides from longest to shortest:
Combined Practice:
Directions: List the sides and angles in order from smallest to largest.
A.
B.
𝐷
C.
85°
7
5
𝐹
𝐸
6
𝐴 45°
𝐴
𝐵
80°
𝐵
30°
𝐸
𝐶
Not every group of 3 segments can form a triangle!
Triangle Inequality Theorem
The ______________ of the lengths of any two sides of a triangle is ____________________ than the
length of the third side.
𝐴
Criteria:
𝐴𝐵 + 𝐵𝐶 > 𝐴𝐶
𝐶
𝐴𝐶 + 𝐵𝐶 > 𝐴𝐵
𝐴𝐵 + 𝐴𝐶 > 𝐵𝐶
𝐵
What the theorem above means..
Practice: Determine if a triangle can have the following sets of side lengths:
1). 3, 5, 7,
2. 8, 13, 21
Finding the Range of Possible Side Lengths:
If you are given the lenths of two sides of a triangle you can find the length of the third side using this:
____________ - ___________ < side< ___________ + _______________
Practice: Determine the range of possible side lengths for the missing side in a triangle.
3. 6, 11
4. 78, 111
Directions: Is it possible to construct a triangle with the given side lengths? If not, explain why.
A. 6, 7, 11
B. 3, 6, 9
C. 35, 120, 120
Example 3: A triangle has one side length of
11 inches and another of 15. Describe the
possible lengths of the third side.
Example 4: A triangle has one side of length
12 and another of length 8. Describe the
possible length of the third side.
Challenge: List the lengths of all 5 segments from least to greatest: