Triangle Inequality theorem

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If a triangle has sides of lengths 5 and 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 (5 - 7) and less than 12 (5 + 7). So, it must be between 2 and 12.

Front

Does the sides 6, 9, 8 make a triangle?

Back

Yes, because 6 + 9 > 8, 6 + 8 > 9, and 9 + 8 > 6.

Tags

CCSS.7.G.A.2

Front

The sum of the lengths of any two sides of a triangle is _____ than the third side.

Back

greater.

Front

If one side of a triangle is 10 and another is 15, what is the maximum length of the third side?

Back

The maximum length of the third side is 24 (10 + 15 - 1).

Front

If a triangle has sides of lengths 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the minimum length of the third side if two sides are 8 and 10?

Back

The minimum length of the third side is 3 (10 - 8 + 1).

Front

If a triangle has sides of lengths 7, 10, and 12, does it form a triangle?

Back

Yes, because 7 + 10 > 12, 7 + 12 > 10, and 10 + 12 > 7.

Tags

CCSS.7.G.A.2

Front

What happens if the sum of two sides is equal to the third side?

Back

The three points are collinear, and they do not form a triangle.

Tags

CCSS.7.G.A.2

Front

If the lengths of two sides are 6 and 15, what are the possible lengths of the third side?

Back

The possible lengths of the third side are between 9 and 21.