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 45 degrees and 60 degrees, what is the measure of the third angle?

Back

The third angle is 75 degrees, since 180 - (45 + 60) = 75.

Front

What is the range of possible lengths for the third side of a triangle with sides measuring 12 and 7?

Back

The range is 5 < x < 19, according to the Triangle Inequality Theorem.

Front

Is it true that the longest side of a triangle is opposite the largest angle?

Back

Yes, this is a true statement according to the properties of triangles.

Front

What is the measure of an angle in a triangle if the other two angles are 34 degrees and 46 degrees?

Back

The measure of the third angle is 100 degrees, since 180 - (34 + 46) = 100.

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 of a triangle and its angles?

Back

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Front

If a triangle has sides measuring 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 5^2 + 12^2 = 13^2.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.