4.7 Triangle Inequalities

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 have sides of lengths 3, 8, and 9?

Back

Yes, because 3 + 8 > 9, 3 + 9 > 8, and 8 + 9 > 3.

Front

Which set of numbers can represent the lengths of the sides of a triangle?

Back

A set of numbers can represent the lengths of the sides of a triangle if they satisfy the Triangle Inequality Theorem.

Front

List the sides of triangle EHT in descending order if the lengths are HT, EH, and TE.

Back

The sides in descending order are HT, EH, TE.

Front

Does a triangle with side lengths 15, 12, and 9 exist?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

In a scalene triangle ABC, if m∠B=45° and m∠C=55°, what is the order of the sides from longest to shortest?

Back

The order of the sides from longest to shortest is BC, AB, AC.

Front

What is a scalene triangle?

Back

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

Front

What is an isosceles triangle?

Back

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

Front

What is an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length.

Front

How do you determine if three lengths can form a triangle?

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side.