5.5 Inequalities in Two Triangles

Front

What is 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 one angle of a triangle is larger than another, what can be said about the lengths of the sides opposite those angles?

Back

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

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

How can you determine which side is the longest in a triangle?

Back

To determine the longest side, compare the measures of the angles; the side opposite the largest angle is the longest.

Front

What does it mean if two triangles have two pairs of congruent angles?

Back

If two triangles have two pairs of congruent angles, they are similar, meaning their corresponding sides are in proportion.

Front

What is the significance of the third angle in a triangle?

Back

The third angle can be determined using the fact that the sum of the angles in a triangle is always 180 degrees.

Front

How do you find the range of possible values for a variable in triangle inequalities?

Back

Use the Triangle Inequality Theorem to set up inequalities based on the lengths of the sides and solve for the variable.

Front

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

Back

In a triangle, the side lengths are proportional to the sine of their opposite angles.

Front

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

Back

The angles opposite the equal sides are also equal, making the triangle isosceles.

Front

What is an example of an inequality involving the sides of a triangle?

Back

For a triangle with sides a, b, and c, the inequalities are: a + b > c, a + c > b, and b + c > a.