Inequalities in Two Triangles (Hinge Theorem)

Front

What is the Hinge Theorem in relation to triangles?

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 angles are not congruent, then the triangle with the larger included angle will have a longer third side.

Front

How can you compare the lengths of sides in two triangles using the Hinge Theorem?

Back

If two triangles have two pairs of corresponding sides that are equal, the triangle with the larger included angle will have the longer third side.

Front

What does it mean if BC > EF in the context of triangles?

Back

It means that side BC of one triangle is longer than side EF of another triangle, which can be determined using the Hinge Theorem.

Front

If two triangles share a common vertex and have sides formed from the radii of a circle, how do you compare the lengths of those sides?

Back

The side opposite the larger angle will be longer; thus, if EF is opposite a smaller angle than FG, then EF < FG.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

In triangles, the larger angle is opposite the longer side, and the smaller angle is opposite the shorter side.

Front

How do you determine which angle is greater when comparing two triangles?

Back

You can determine which angle is greater by comparing the lengths of the sides opposite those angles; the angle opposite the longer side is greater.

Tags

CCSS.HSG.CO.C.10

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 third sides of the triangles when the other two sides are equal.

Front

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

Back

The side opposite Angle 1 will be longer than the side opposite Angle 2.

Tags

CCSS.HSG.CO.C.10

Front

What is the implication of two triangles having two sides equal and one angle unequal?

Back

If two triangles have two sides equal and one angle unequal, the triangle with the larger angle will have a longer third side.

Tags

CCSS.8.G.A.2

Front

How can the Hinge Theorem be applied in real-world problems?

Back

The Hinge Theorem can be used in various applications such as engineering, architecture, and design, where the relationships between angles and sides of triangles are critical.