Triangle Inequalities and Hinge Theorem

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

How do you determine the smallest angle in a triangle?

Back

The smallest angle in a triangle is located across from the smallest side.

Tags

CCSS.HSG.CO.C.10

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Front

If a triangle has sides of lengths 7, 10, and x, what is the range of possible values for x?

Back

x must be greater than 3 and less than 17.

Front

What can you conclude if one angle of a triangle is larger than another?

Back

The side opposite the larger angle is longer than the side opposite the smaller angle.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

Yes, a triangle with these side lengths can exist.

Tags

CCSS.7.G.A.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 side opposite that angle.

Tags

CCSS.HSG.CO.C.10

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 maximum length of the third side in a triangle with sides of lengths 8 and 6?

Back

The maximum length of the third side is less than 14.

Front

What is the minimum length of the third side in a triangle with sides of lengths 8 and 6?

Back

The minimum length of the third side is greater than 2.