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

If two angles of a triangle are 50 degrees and 60 degrees, what is the measure of the third angle?

Back

The third angle is 70 degrees, since 180 - (50 + 60) = 70.

Front

Given two sides of lengths 8 and 15, what is the range of possible lengths for the third side?

Back

The range is 7 < x < 23, according to the Triangle Inequality Theorem.

Front

What is the largest angle in a triangle with sides of lengths 5, 12, and 13?

Back

The largest angle is opposite the longest side, which is 13.

Front

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

Back

It is a right triangle.

Front

How do you find the range of possible lengths for the third side of a triangle given two sides of lengths a and b?

Back

The range is given by |a - b| < x < a + b.

Front

What is the measure of an angle in a triangle if the other two angles are 30 degrees and 60 degrees?

Back

The measure of the third angle is 90 degrees, since 180 - (30 + 60) = 90.

Front

In a triangle with sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, it is a right triangle because 7^2 + 24^2 = 25^2.

Front

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

Back

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