Triangle Inequalities and Hinge Theorem

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 12 meters and 7 meters, what is the range of possible lengths for the third side?

Back

5 < x < 19

Front

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

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

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 side lengths are 7, 5, and 4, can they form a triangle?

Back

Yes, because 7 + 5 > 4, 7 + 4 > 5, and 5 + 4 > 7.

Front

What is the longest side in a triangle?

Back

The longest side is always opposite the largest angle.

Front

How do you determine if a triangle is valid based on its side lengths?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side.

Front

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

Back

It is an isosceles triangle.

Front

What is the range of possible lengths for the third side if two sides are 10 and 6?

Back

4 < x < 16.