Hinge Theorem

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, then the angles opposite the longer third side are greater.

Front

If two sides of a triangle are equal, what can be said about the angles opposite those sides?

Back

The angles opposite the equal sides are also equal.

Tags

CCSS.8.G.A.5

Front

In the context of the Hinge Theorem, if segment AC is longer than segment AB, what can be said about the angle opposite segment AC compared to the angle opposite segment AB?

Back

The angle opposite segment AC is greater than the angle opposite segment AB.

Tags

CCSS.HSG.CO.C.9

Front

What is the relationship between the lengths of sides and the angles in a triangle according to the Hinge Theorem?

Back

In a triangle, the larger the length of a side, the larger the angle opposite that side.

Front

Given two triangles with sides of lengths 5, 7, and 9, and 5, 8, and 10, which triangle has the larger angle opposite the longest side?

Back

The second triangle has the larger angle opposite the longest side.

Tags

CCSS.HSG.CO.C.10

Front

If angle 1 is greater than angle 2, what can be inferred about the lengths of the sides opposite these angles?

Back

The side opposite angle 1 is longer than the side opposite angle 2.

Tags

CCSS.HSG.CO.C.10

Front

What is the range of possible values for x if the sides of a triangle are 5, 7, and x?

Back

Front

If angle 1 is 30 degrees and angle 2 is 45 degrees, which side is longer?

Back

The side opposite angle 2 is longer.

Front

How can the Hinge Theorem be applied to determine the possible lengths of a triangle's side?

Back

By comparing the lengths of two sides and their opposite angles, one can determine the range of possible lengths for the third side.

Front

What is the significance of the longest side in a triangle?

Back

The longest side is always opposite the largest angle.