5.5 Inequalities in two triangles

Front

What is an inequality in the context of triangles?

Back

An inequality in triangles refers to the relationship between the lengths of the sides and the measures of the angles. For example, in any triangle, the side opposite the largest angle is the longest side.

Front

State the Triangle Inequality Theorem.

Back

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

Front

If two angles of a triangle are equal, what can be said about the sides opposite those angles?

Back

The sides opposite the equal angles are also equal in length.

Front

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

Back

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

Front

How can you determine if one triangle is larger than another based on their angles?

Back

If one triangle has a larger angle than another triangle, the side opposite the larger angle will be longer, indicating that the triangle is larger.

Front

What does it mean if one side of a triangle is longer than another?

Back

If one side of a triangle is longer than another, the angle opposite the longer side is larger than the angle opposite the shorter side.

Front

Back

The angle opposite side AC is larger than the angle opposite side DF.

Front

What is the significance of the shortest side in a triangle?

Back

The shortest side of a triangle is always opposite the smallest angle.

Front

Back

Front

Back