Triangle Inequalities

Front

Can a triangle be formed with side lengths: 10, 12, 22?

Back

No, because the sum of the lengths of the two shorter sides (10 + 12 = 22) is not greater than the length of the longest side (22). This violates the triangle inequality theorem.

Front

Where is the smallest angle located in a triangle?

Back

Across from the smallest side.

Front

Order the angles from SMALLEST to LARGEST: Q, R, P.

Back

R, P, Q.

Front

Solve for x in the triangle inequality: x + 5 > 12.

Back

x > 7.

Front

Where is the longest side of a triangle located?

Back

Across from the largest angle.

Front

What is the triangle inequality theorem?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

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

Back

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

Front

If the sides of a triangle are 5, 12, and 13, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (5^2 + 12^2 = 13^2).

Front

What is the minimum length of the third side if two sides of a triangle are 8 and 10?

Back

The minimum length of the third side must be greater than 2 (10 - 8).