Triangle Inequalities

Front

Can a triangle be formed with side lengths: 17, 9, 30?

Back

No, because the sum of the lengths of the two shorter sides (17 + 9 = 26) is less than the length of the longest side (30). This violates the triangle inequality theorem.

Front

Name the angles from LARGEST to SMALLEST for a triangle with angles R, S, T.

Back

R, S, T. The largest angle corresponds to the longest side.

Front

What is an angle bisector?

Back

An angle bisector is a line that splits any angle in half, creating two equal angles.

Front

Order the sides from least to greatest for sides DE, VE, DV.

Back

DE, VE, DV. This is based on the lengths of the sides.

Front

Can a triangle be formed with side lengths: 4, 7, 10?

Back

Yes, because the sum of the lengths of the two shorter sides (4 + 7 = 11) is greater than the length of the longest side (10). This satisfies the triangle inequality theorem.

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

If one side of a triangle is 8 and another is 5, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 (8 - 5) and less than 13 (8 + 5). So, the range is (3, 13).

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

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

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.