Triangle Angle Side Relationship

Front

What is the Triangle Angle-Side Relationship?

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

How do you determine the largest angle in a triangle?

Back

The largest angle is opposite the longest side of the triangle.

Front

How do you determine the smallest angle in a triangle?

Back

The smallest angle is opposite the shortest side of the triangle.

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

Given two sides of lengths 2 and 6, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 4 and less than 8.

Front

Can a triangle have sides of lengths 3, 4, and 9?

Back

No, because the sum of the lengths of the two shorter sides (3 + 4 = 7) is less than the length of the longest side (9).

Front

In triangle ∆XYZ, if m∠x = 40°, m∠y = 60°, and m∠z = 80°, which side is the longest?

Back

Side XY is the longest because it is opposite the largest angle (80°).

Front

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

Back

The angles and sides of a triangle are directly related; larger angles correspond to longer opposite sides.

Front

How can you find the measure of an unknown angle in a triangle?

Back

You can use the fact that the sum of the angles in a triangle is always 180°. Subtract the sum of the known angles from 180°.

Front

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

Back

The sum of the interior angles of a triangle is 180°.