5-4 Inequalities In One Triangle

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 two angles of a triangle are known, how can you find the third angle?

Back

The third angle can be found using the formula: Third Angle = 180° - (Angle 1 + Angle 2).

Front

How do you determine the order of angles in a triangle based on their opposite sides?

Back

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

Front

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

Back

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

Front

Can a triangle have sides of lengths 3, 4, and 8?

Back

No, because 3 + 4 is not greater than 8, violating the Triangle Inequality Theorem.

Front

What is the range of possible lengths for the third side of a triangle with sides of lengths 5 and 13?

Back

The possible lengths for the third side (x) must satisfy 8 < x < 18.

Front

What is the definition of an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is the definition of an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle equal to 90 degrees.

Front

How can you determine if a triangle is isosceles?

Back

A triangle is isosceles if it has at least two sides of equal length.