3.1 Triangle Sum & Triangle Inequality

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

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

How do you determine the smallest angle in a triangle?

Back

To determine the smallest angle in a triangle, identify the side with the smallest length; the angle opposite this side will be the smallest.

Front

If one angle of a triangle measures 30 degrees and another measures 60 degrees, what is the measure of the third angle?

Back

The third angle measures 90 degrees, since 30 + 60 + 90 = 180 degrees.

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Front

How can you order the sides of a triangle based on their opposite angles?

Back

Order the sides from least to greatest based on the angles opposite them; the smallest angle corresponds to the shortest side.

Front

What is the measure of the angles in an equilateral triangle?

Back

In an equilateral triangle, all three angles measure 60 degrees.

Front

What is the measure of the angles in an isosceles triangle?

Back

In an isosceles triangle, the two angles opposite the equal sides are equal, and the sum of all angles is 180 degrees.

Front

How do you find the measure of an angle when two angles are known?

Back

Subtract the sum of the known angles from 180 degrees to find the measure of the unknown angle.

Front

What is the significance of the angle measures in determining triangle type?

Back

The type of triangle can be classified as acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°) based on its angle measures.