Triangle Inequalities & Algebra

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 the lengths of two sides of a triangle are 8 cm and 10 cm, what is the range of possible lengths for the third side?

Back

The range of possible lengths for the third side is: 2 cm < third side < 18 cm.

Front

What is the relationship between the angles and sides of 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

How do you determine the smallest angle in a triangle?

Back

The smallest angle in a triangle is opposite the shortest side.

Front

In triangle ∆ABC, if ∠A = 30° and ∠B = 60°, what can you say about the lengths of sides a and b?

Back

Since ∠A < ∠B, it follows that side a < side b.

Front

What is the formula to find the range of the third side of a triangle given two sides a and b?

Back

The range of the third side c is: |a - b| < c < a + b.

Front

If ∠C > ∠F, what can be inferred about the lengths of sides opposite these angles?

Back

If ∠C > ∠F, then the length of the side opposite ∠C is greater than the length of the side opposite ∠F.

Front

Back

This inequality ensures that a triangle can be formed with sides of lengths a, b, and c.

Front

In triangle ∆XYZ, if the lengths of sides XY = 7 cm and XZ = 10 cm, what is the maximum possible length for side YZ?

Back

The maximum possible length for side YZ is 17 cm (since 7 + 10 > YZ).

Front

What does it mean if two angles in a triangle are equal?

Back

If two angles in a triangle are equal, the triangle is isosceles, and the sides opposite those angles are also equal.