Geometry:Inequalities in ONE triangle

Front

Will the side lengths 5, 6, 12 make a triangle?

Back

No, because the sum of the lengths of the two shorter sides (5 + 6 = 11) is less than the length of the longest side (12). This violates the triangle inequality theorem.

Front

What is the total sum of the angles in a triangle?

Back

180 degrees.

Front

Name the sides from SMALLEST to LARGEST: 5, 6, 12.

Back

5, 6, 12.

Front

In a triangle, which angle is the smallest if the sides are 5, 6, and 12?

Back

The smallest angle is opposite the shortest side, which is ∠A.

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

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

Back

In a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.

Front

How do you determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: For lengths a, b, and c, they can form a triangle if a + b > c, a + c > b, and b + c > a.

Front

What is an obtuse triangle?

Back

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

Front

What is an acute triangle?

Back

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