Triangle Inequality Flashcard

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

Given sides a, b, and c of a triangle, what conditions must be satisfied according to the Triangle Inequality Theorem?

Back

The conditions are: a + b > c, a + c > b, and b + c > a.

Front

If side lengths of a triangle are 10 inches, 17 inches, and x inches, what is the range of possible values for x?

Back

x must satisfy: |10 - 17| < x < 10 + 17, which simplifies to 7 < x < 27.

Front

How do you determine the order of angles in a triangle based on side lengths?

Back

The angles opposite the shorter sides are smaller, and the angles opposite the longer sides are larger.

Front

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

Back

In a triangle, the larger the side, the larger the opposite angle, and vice versa.

Front

Can a triangle be formed with side lengths 17, 9, and 30? Why or why not?

Back

No, because 17 + 9 is not greater than 30, violating the Triangle Inequality Theorem.

Front

How do you list the sides of a triangle from smallest to largest?

Back

To list the sides from smallest to largest, compare the lengths of each side and arrange them in ascending order.

Front

What is the significance of the longest side in a triangle?

Back

The longest side is always opposite the largest angle in the triangle.

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 definition of a scalene triangle?

Back

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