5.6 Inequalities in One Triangle

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

Can a triangle be formed with sides of lengths 15, 8, and 7?

Back

No, because 15 is not less than the sum of 8 and 7.

Front

List the sides of a triangle with lengths 6, 9, and 11 from smallest to largest.

Back

The sides in order are: 6, 9, 11.

Front

Is it possible to construct a triangle with sides 15, 37, and 53?

Back

No, because 15 + 37 is not greater than 53.

Front

Where is the largest angle of a triangle located?

Back

The largest angle is located across from the longest side.

Front

Can a triangle be formed with sides of lengths 6, 9, and 11?

Back

Yes, because 6 + 9 > 11, 6 + 11 > 9, and 9 + 11 > 6.

Front

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

Back

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

Front

If a triangle has sides of lengths 5, 12, and 13, can it be classified as a right triangle?

Back

Yes, because 5^2 + 12^2 = 13^2.

Front

What is the definition of a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides have different lengths.

Front

What is the definition of an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.