Inequalities in 2 Triangles (Section 5-6)

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 angles are not equal, then the triangle with the larger included angle has the longer third side.

Front

What does the SAS Inequality state?

Back

The SAS Inequality 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 QT < ST, what can be inferred about the angles opposite these sides?

Back

If QT < ST, then the angle opposite QT (Angle Q) is less than the angle opposite ST (Angle S).

Front

What is the relationship between the sides and angles in triangles?

Back

In triangles, the larger the angle, the longer the side opposite that angle. Conversely, the smaller the angle, the shorter the side opposite that angle.

Front

What is the significance of the vertex in the Hinge Theorem?

Back

The vertex of the angle acts like a hinge, allowing the triangle to open or close, which affects the lengths of the opposite sides.

Front

If BC > EF, what can be concluded about the angles opposite these sides?

Back

If BC > EF, then the angle opposite BC is greater than the angle opposite EF.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Front

What does the term 'included angle' refer to in triangle geometry?

Back

The included angle is the angle formed between two sides of a triangle.

Front

How can you determine if two triangles are congruent using the SAS postulate?

Back

Two triangles are congruent by the SAS postulate if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is also equal.

Front

What is the relationship between the sides of a triangle and the angles opposite them?

Back

The relationship is such that the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.