5.6 Hinge Theorem

The Hinge Theorem states that if two triangles have two sides of equal length, the larger angle is opposite the longer third side.

The triangle with the longer third side will have the larger angle opposite to it.

It can be inferred that $$m\angle BAC > m\angle EDF$$ .

It means that angle BAC is larger than angle EDF, indicating that side AC is shorter than side DF.

It implies that the sides opposite those angles are equal in length.

The side opposite the larger angle is the longer side.

The relationship is that larger angles correspond to longer opposite sides.

It can be concluded that $$m\angle BAC > m\angle EDF$$ .

Comparing angles helps determine the relative lengths of the opposite sides.

Shawn's locker is farther away from the reference point than Neva's.