Triangle Inequalities and Hinge Theorem Review

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 a triangle has sides of lengths 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

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

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

Which side is shorter in a triangle with sides 5, 7, and 10?

Back

The shorter sides are 5 and 7, with 5 being the shortest.

Front

In a triangle, if one angle measures 60 degrees and another measures 80 degrees, what can be said about the lengths of the sides opposite these angles?

Back

The side opposite the 80-degree angle is longer than the side opposite the 60-degree angle.

Front

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

Back

In a triangle, larger angles are opposite longer sides.

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 maximum length of a side in a triangle with sides of lengths 4 and 6?

Back

The maximum length of the third side must be less than 10 (4 + 6) and greater than 2 (6 - 4).

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 (10 - 7) and less than 17 (7 + 10).