Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If two sides of a triangle are 3 and 5, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 (3-5) and less than 8 (3+5). So, it can be any length between 2 and 8.

Front

Which of the following lengths can form a triangle with sides 4 and 7? 10, 11, 12, 13

Back

10 and 11 can form a triangle. The third side must be less than 11 (4+7) and greater than 3 (7-4).

Tags

CCSS.7.G.A.2

Front

Can the lengths 5, 5, and 10 form a triangle?

Back

No, because 5 + 5 is not greater than 10.

Tags

CCSS.7.G.A.2

Front

What is the minimum length of the third side if the other two sides are 6 and 8?

Back

The minimum length of the third side must be greater than 2 (8-6).

Front

If the longest side of a triangle is 12, what must be true about the other two sides?

Back

The sum of the other two sides must be greater than 12.

Front

Which of the following sets of lengths can form a triangle? 3, 4, 5; 1, 2, 3; 6, 8, 15

Back

3, 4, 5 can form a triangle. 1, 2, 3 cannot form a triangle. 6, 8, 15 cannot form a triangle.

Tags

CCSS.7.G.A.2

Front

What happens if one side of a triangle is equal to the sum of the other two sides?

Back

It does not form a triangle; it forms a straight line.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Tags

CCSS.4.G.A.2

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.