Angle-Side Relationship & Triangle Inequality

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

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

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

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

Back

It is an isosceles triangle.

Front

What is the maximum length of the third side of a triangle with sides 5 and 7?

Back

The maximum length is less than 12 (5 + 7 - 1).

Front

What is the minimum length of the third side of a triangle with sides 5 and 7?

Back

The minimum length is greater than 2 (7 - 5 + 1).

Front

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

Back

Yes, because 8 + 15 > 17, 8 + 17 > 15, and 15 + 17 > 8.

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.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle equal to 90 degrees.