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 12 and 7, what is the range of possible measures for the third side?

Back

The third side must be greater than 5 and less than 19.

Front

Can the sides 9, 3, and 10 form a triangle?

Back

Yes, because 9 + 3 > 10, 9 + 10 > 3, and 3 + 10 > 9.

Tags

CCSS.7.G.A.2

Front

Can the sides 11, 7, and 21 form a triangle?

Back

No, because 11 + 7 < 21.

Tags

CCSS.7.G.A.2

Front

Can the sides 18, 7, and 10 form a triangle?

Back

No, because 18 + 7 < 10.

Tags

CCSS.7.G.A.2

Front

Can the sides 8, 10, and 20 form a triangle?

Back

No, because 8 + 10 < 20.

Tags

CCSS.7.G.A.2

Front

What must be true for three lengths to form a triangle?

Back

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

Front

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

Back

The third side must be greater than 5 and less than 25.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

Lengths 5, 2, and 8 cannot form a triangle because 5 + 2 < 8.

Tags

CCSS.7.G.A.2

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps determine whether a set of three lengths can form a triangle, which is fundamental in triangle construction and properties.