Download Triangle Inequality Theorem

Triangle Angle Sum Theorem
This theorem states that the sum of the angles in any triangle is 180⁰.
This means that before any triangle can be form, we have to make sure their angles add up to be
180⁰.
_________________________INDEPENDENPENT PRACTICE___________________
1. Tom drew ∆NET, which is shown
below.
3. Derek drew the following triangle:
What is the name of this triangle?
Based on the information in the
triangle, what type is it?
A. Acute Scalene triangle
A. Right
C. Scalene
B. Acute
D. Obtuse
4. Ciara constructs a triangle with
angles measuring 65⁰ and 38⁰. What
must be true of the measure of the
third angle in her construction?
B. Obtuse Isosceles triangle
A. It must measure exactly 77⁰
C. Acute Isosceles triangle
B. It must measure exactly 87⁰
C. It can have measure less than 103⁰
D. Right Triangle
2. Which of the following set of angle
measures would make a triangle?
A. 10⁰, 50⁰, 70⁰
C. 100⁰,60⁰,30⁰
B. 100⁰,50⁰,30⁰
D. 80⁰, 90⁰,20⁰
D. It can have any measure greater than
27⁰
5.. Below is a yield sign:
7. When drawing the triangle PIN,
Ericka wants to find the measure of
the missing angle.
If all the sides are congruent, what
type triangle is it?
A. 40⁰
A. Equilateral
B. 60⁰
B. Scalene
C. Obtuse
D. Isosceles
6. One day, Mrs. Carter, Coach
Lombard, Mr. Hill, and Mrs.
Blackledge went for a trail walk for
some exercise. The path they walked
is shown below.
C. 30⁰
D. 50⁰
8. What statement is true about
Isosceles triangles?
A. They have two congruent sides
only
B. They have no sides congruent but
all angles congruent
C. They have congruent sides and
congruent angles
D. They have two congruent sides and
two congruent angles
Their route resembles a
A. Right Triangle
B. Obtuse Triangle
C. Straight Triangle
D. Acute Triangle
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the
third side.
x+y>z
x+z>y
y+z>x
COACHED EXAMPLE
Is it possible to construct a triangle with sides measuring 8 feet, 9 feet, and 12 feet?
The triangle inequality theorem states that sum of the lengths of any two sides of a
triangle must be________________________ than the length of the third side.
Use the theorem to determine if this triangle is possible or not.
Is 8 + 9 > 12?______________________________
Is 8 + 12 > 9?______________________________
Is 9 + 12 > 8?______________________________
The inequalities above are all true, so it____________possible to draw a triangle
with side lengths of 8 feet, 9 feet, and 12 feet.
Lets explore these for ourselves by completing some practice.
For questions 1-6, tell whether a triangle can be constructed using the give measure
1. 2 in, 2 in, 3 in
4. 8 in, 7 in, 15 in
2. 3 ft, 15 ft, 9ft
5. Lincoln constructs a triangle with
one side 5 inches long and another
side 7 inches long. Which is not a
possible length for the third side?
A. 3 inches
B. 6 inches
C. 11 inches
D. 12 inches
3. 4 yd, 6 yd, 5 yd
6. Maggie constructs a triangle with
one side 7 centimeters long and
another side 10 centimeters long.
Which is not a possible length for the
third side?
A. 2 centimeters
B. 4 centimeters
C. 7 centimeters
D. 16 centimeters