5.6 Hinge Theorem

Front

What is the Hinge Theorem?

Back

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

Front

If two triangles have equal sides, how do their angles compare?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

In triangle ABC and triangle EDF, if AC < DF, what can be inferred about the angles?

Back

Tags

CCSS.HSG.CO.B.7

Front

Back

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

Tags

CCSS.HSG.CO.C.10

Front

If two angles are congruent, what does that imply about the sides opposite them?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

How can you determine which side is longer in a triangle using angles?

Back

The side opposite the larger angle is the longer side.

Front

What is the relationship between angles and sides in triangles according to the Hinge Theorem?

Back

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

Front

If triangle ABC has sides AC and AB, and triangle EDF has sides DF and DE, what can be said if AC < DF?

Back

Front

What is the significance of comparing angles in the Hinge Theorem?

Back

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

Front

If Neva's locker forms a smaller angle than Shawn's, what can be inferred about their distances?

Back

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