Triangle Inequality Theorem Review

Triangle Inequality Theorem

Can we make a triangle?

Angle Sum of a Triangle

• The sum of the measures of the interior angles of a triangle is 180^o.

• <1 + <2 + <3 = 180

Remember:
You can make multiple triangles of different sizes with one set of angles.
However, if you are given a set of side lengths, you are given the dimensions of a single triangle.

Notice the greater than symbol! It is NOT the greater than or equal to symbol.

Why do I need to know this?

• Sometimes you will NOT be given a picture and you have to determine if you can create a triangle given the number lengths provided.

• Example: Given the lengths 2, 5, and 8cm, can you create a triangle?

What if the sum equals the other side?

• Ex: 2, 5, 7 are given and if you add 2 + 5 you get 7.... 7 is not greater than 7, so you CANNOT create a triangle.

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Example of proving a triangle can be made with the given side lengths of 7, 8, and 9.

Example of proving a triangle cannot be made with the given side lengths of 4, 8, and 2.

Multiple Choice

Which set of side lengths will make a triangle?

• 6, 8, 13
• 7, 9, 18
• 7, 7, 14
• 2, 6, 9

Multiple Choice

How many triangles exist with the following angle measures?
80°, 50°, 50°

• No triangle exists with the given angle measures.
• More than one unique triangle exists with the given angle measures.
• Exactly one unique triangle exists with the given angle measures.

Multiple Choice

Does a triangle with these side lengths exist?
33, 16, 17

• Yes
• No
• I don't know.

Multiple Choice

Which would be the best classification for the triangle shown?

• right isosceles
• obtuse scalene
• obtuse isosceles
• acute scalene

Multiple Choice

Which set of side lengths will NOT make a triangle?

• 3, 4, 5
• 1, 3, 4
•  3, 5, 7
• 2, 8, 9

Multiple Choice

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

Multiple Choice

Can the sides of a triangle have lengths 4, 11, and 13?

• Yes

• No

Multiple Choice

Can the following side measures form a triangle?

3, 5, 8

• Yes

• No