Coach E's Hinge Theorem Flashcard

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

How do you identify the largest angle in a triangle?

Back

The largest angle in a triangle is opposite the longest side.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, which is a criterion for triangle congruence stating that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, which is a criterion for triangle congruence stating that if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

Where is the smallest angle located in a triangle?

Back

The smallest angle is located across from the smallest side.

Front

If two triangles have two sides equal and the included angle of one is larger, what can be said about the third side?

Back

The third side of the triangle with the larger included angle will be longer.

Front

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

Back

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

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If segment AC has possible lengths of 10, 15, 17, and 9, which is valid?

Back

17 is a valid length for segment AC, assuming it satisfies the triangle inequality with the other sides.

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is significant because it helps determine the relationship between the sides of the triangles, especially in SAS.