Inequalities in Triangles

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

Can the sides of a triangle have lengths 3, 8, and 9?

Back

Yes, because 3 + 8 > 9, 3 + 9 > 8, and 8 + 9 > 3.

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

If the given side lengths of a triangle are 16 and 10, what can be the range for the third side?

Back

The third side must be greater than |16 - 10| = 6 and less than 16 + 10 = 26. So, it can be between 6 and 26.

Front

Which side lengths would NOT form a triangle? {2,5,9}, {3,4,5}, {5,10,12}, {7,9,11}

Back

{2,5,9} because 2 + 5 is not greater than 9.

Front

Name the smallest angle in a triangle with sides 5, 6, and 7.

Back

The smallest angle is opposite the shortest side, which is 5.

Front

Name the largest angle in a triangle with sides 8, 10, and 12.

Back

The largest angle is opposite the longest side, which is 12.

Front

What is the sum of the angles in any triangle?

Back

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

Front

If two angles of a triangle are 30° and 70°, what is the third angle?

Back

The third angle is 180° - (30° + 70°) = 80°.

Front

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.