Hinge theorem review

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of one triangle 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

How do you determine the longest side of a triangle using angles?

Back

The longest side of a triangle is opposite the largest angle. To determine the longest side, compare the measures of the angles.

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

If two sides of a triangle are 14 cm and 19 cm, what is the range for the length of the third side?

Back

The length of the third side must be greater than |14 - 19| = 5 cm and less than 14 + 19 = 33 cm. Therefore, the possible lengths are between 5 cm and 33 cm.

Front

Can a triangle have sides measuring 4 cm, 7 cm, and 2 cm?

Back

No, because 4 + 2 is not greater than 7, violating the Triangle Inequality Theorem.

Front

How do you order angles in a triangle from largest to smallest?

Back

To order angles from largest to smallest, compare their measures. The angle with the largest measure is first, followed by the second largest, and then the smallest.

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

If angle Y is greater than angle M, what can be said about the sides opposite these angles?

Back

The side opposite angle Y is longer than the side opposite angle M.

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

How do you find the measure of an unknown angle in a triangle?

Back

To find an unknown angle, subtract the sum of the known angles from 180 degrees.