5.6 Inequalities in Two Triangles

Front

What is an inequality in the context of triangles?

Back

An inequality in the context of triangles refers to the relationship between the lengths of the sides of a triangle, where the sum of the lengths of any two sides must be greater than the length of the third side.

Front

State the Triangle Inequality Theorem.

Back

The Triangle Inequality Theorem states that for any triangle with sides of lengths a, b, and c, the following inequalities must hold: a + b > c, a + c > b, and b + c > a.

Front

How do you determine if a triangle can be formed with given side lengths?

Back

To determine if a triangle can be formed with given side lengths, check if the lengths satisfy the Triangle Inequality Theorem.

Front

Back

The range of possible values for x is all real numbers greater than -3/5 and less than 7.

Front

Back

The possible values of x are all real numbers less than 21.

Front

What does it mean if a triangle cannot be formed with given side lengths?

Back

If a triangle cannot be formed with given side lengths, it means that the lengths do not satisfy the Triangle Inequality Theorem.

Front

What is the significance of the range of values for x in inequalities?

Back

The range of values for x in inequalities indicates all possible solutions that satisfy the given conditions.

Front

Back

The possible values for x are all real numbers greater than 4 and less than 16.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. This is known as the Angle-Side Relationship.

Front

How do you express the range of possible values for x in an inequality?

Back

The range of possible values for x in an inequality is expressed using inequality symbols, such as <, >, ≤, or ≥.