Inequalities in Two Triangles (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, 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

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 triangles, what does it mean for one angle to be greater than another?

Back

It means that the side opposite the greater angle is longer than the side opposite the smaller angle.

Tags

CCSS.HSG.CO.C.10

Front

If triangle ABC has sides AB and AC, and triangle DEF has sides DE and DF, what can be concluded if AB = DE and AC < DF?

Back

Angle A < Angle D according to the Hinge Theorem.

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Tags

CCSS.HSG.CO.C.10

Front

How can you determine if one triangle is larger than another using the Hinge Theorem?

Back

By comparing the lengths of two sides and the included angle of each triangle.

Front

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

Back

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

Tags

CCSS.HSG.CO.C.10

Front

What does it mean if two triangles are said to be congruent?

Back

It means that all corresponding sides and angles of the triangles are equal.

Tags

CCSS.8.G.A.2

Front

If two triangles share a common side and have two equal angles, what can be said about their third sides?

Back

The third sides are equal according to the properties of congruent triangles.

Tags

CCSS.8.G.A.2

Front

What is the significance of the included angle in the Hinge Theorem?

Back

The included angle is crucial because it determines the relationship between the lengths of the opposite sides.

Tags

CCSS.HSG.CO.B.7