Inequalities in Triangles

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

If two sides of a triangle are 8 and 10, what is the range of possible lengths for the third side?

Back

The range of possible lengths for the third side is 2 < x < 18.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

What cannot be the length of the third side if the other two sides are 5 and 7?

Back

The third side cannot be 13, as 5 + 7 must be greater than the third side.

Front

Define an obtuse triangle.

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.

Front

If the sides of a triangle are 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (3^2 + 4^2 = 5^2).

Front

What is the minimum length of the third side if two sides are 6 and 10?

Back

The minimum length of the third side must be greater than 4 (10 - 6).

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

If a triangle has angles of 30° and 60°, what is the measure of the third angle?

Back

The third angle measures 90°, as the sum of angles in a triangle is 180°.