Topic #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

List the angles of a triangle in order from smallest to largest based on their side lengths.

Back

The angles of a triangle are opposite to the sides. The smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.

Tags

CCSS.HSG.CO.C.10

Front

If two sides of a triangle are 9 and 7, what is the range of possible lengths for the third side?

Back

The range for the third side x is: 2 < x < 16.

Front

Can a triangle exist with side lengths 15, 12, and 9?

Back

Yes, because the sum of the lengths of any two sides is greater than the length of the third side.

Tags

CCSS.7.G.A.2

Front

Which of the following sets can represent the lengths of the sides of a triangle: {2,5,9}, {6,6,7}, {6,4,2}, {7,8,1}?

Back

Only {6,6,7} can represent the lengths of the sides of a triangle.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Tags

CCSS.4.G.A.2

Front

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

Back

The minimum length of the third side is greater than 0.

Front

What is the maximum length of the third side if the other two sides are 9 and 9?

Back

The maximum length of the third side is less than 18.

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.

Tags

CCSS.HSG.CO.C.10

Front

How do you determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: the sum of the lengths of any two sides must be greater than the length of the third side.