Section 5-6: 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 angles of a triangle, often expressed as a range of possible values for a side length based on the lengths of the other sides.

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 sides of a triangle are 7 and 10, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than the difference of the two sides and less than the sum of the two sides: 3 < x < 17.

Front

What does it mean if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

How can you determine if two triangles are congruent?

Back

Two triangles are congruent if they have the same size and shape, which can be established through criteria such as SSS (Side-Side-Side), SAS (Side-Angle-Side), or ASA (Angle-Side-Angle).

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

Back

Front

What is the significance of the angle-side relationship in triangles?

Back

The angle-side relationship in triangles is significant because it helps in determining the possible lengths of sides based on the angles, which is crucial for solving problems involving triangle inequalities.

Front

Define the term 'congruent triangles'.

Back

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

Front

What is the difference between 'similar' and 'congruent' triangles?

Back

Similar triangles have the same shape but not necessarily the same size (proportional sides), while congruent triangles are identical in both shape and size.