Unit 4 Day 9 Triangle Inequalities

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The third side must be greater than 2 (5 - 7) and less than 12 (5 + 7). So, the range is (2, 12).

Front

Can a triangle have sides of lengths 8, 3, and 10?

Back

No, because 8 + 3 is not greater than 10.

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 a triangle has sides of lengths 6, 8, and x, what is the maximum value of x?

Back

x must be less than 14 (6 + 8). So, the maximum value of x is 13.

Front

What is the minimum length of the third side if two sides are 9 and 4?

Back

The minimum length of the third side must be greater than 5 (9 - 4). So, it must be at least 6.

Front

In a triangle with sides 7, 10, and 12, which angle is the largest?

Back

The angle opposite the side of length 12 is the largest.

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

Back

It is a right triangle.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.