Inequalities in Two Triangles

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two sides of one triangle are 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 one triangle are congruent to two sides of another triangle, what can be said about the included angles?

Back

If the included angle of the first triangle is larger than that of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

Front

Back

It means that angle C is larger than angle F.

Front

What is the relationship between the sides of triangles when one angle is larger than another?

Back

The side opposite the larger angle is longer than the side opposite the smaller angle.

Front

What is the significance of congruent sides in triangles?

Back

Congruent sides indicate that the triangles may have a specific relationship regarding their angles and other sides, often used in the Hinge Theorem.

Front

How can you determine the length of a side in a triangle using angles?

Back

By comparing the angles, you can determine that the side opposite the larger angle is longer than the side opposite the smaller angle.

Front

What is the inequality relationship in triangles based on angles?

Back

In any triangle, if one angle is larger than another, the side opposite the larger angle is longer than the side opposite the smaller angle.

Front

Back

It implies that the side AC is longer than the side DF.

Front

What is the purpose of inequalities in triangle comparisons?

Back

Inequalities help to establish relationships between the lengths of sides and the measures of angles in triangles.

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