Hinge Theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two sides of equal length, the triangle with the larger included angle will have a longer third side.

Front

According to the triangle inequality theorem, any side of a triangle must be _______ the other two sides of the triangle combined.

Back

shorter than

Front

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

Back

11 cm

Front

Can a triangle be formed with line segments that have lengths 2, 8, and 14 units?

Back

No, because these line segments wouldn't satisfy the triangle inequality theorem.

Front

List the sides of triangle BCD from least to greatest if m< B = 10x - 28, m<C = 6x-1, and m< D = 8x -7.

Back

BD, CD, BC

Front

Using the hinge theorem, we can say that Angle 1 _____ Angle 2.

Back

Greater than

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 one side of a triangle is 10 cm and the other is 15 cm, what is the range of possible lengths for the third side?

Back

The third side must be greater than 5 cm and less than 25 cm.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, which means their corresponding sides and angles are equal.

Front

How can you determine if a triangle is obtuse using the Hinge Theorem?

Back

If one angle is greater than 90 degrees, the side opposite that angle will be longer than the sides opposite the other angles.