Triangle Inequalities

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

What is the range of possible lengths for the third side of a triangle with sides of lengths 5 and 7?

Back

The third side must be greater than 2 (5 - 7) and less than 12 (5 + 7). So, the range is (2, 12).

Front

If a triangle has sides of lengths 8, 15, and 17, does it satisfy the Triangle Inequality Theorem?

Back

Yes, it satisfies the theorem because 8 + 15 > 17, 8 + 17 > 15, and 15 + 17 > 8.

Front

Where is the smallest angle located in a triangle?

Back

The smallest angle is located across from the smallest side.

Front

Where is the largest angle located in a triangle?

Back

The largest angle is located across from the longest side.

Front

Can a triangle have sides of lengths 2, 3, and 6?

Back

No, because 2 + 3 is not greater than 6.

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, the larger the side, the larger the opposite angle.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all angles are less than 90 degrees.