Triangle Properties and Theorems

The video covers the Pythagorean Inequalities Theorem, explaining how to classify triangles as acute, obtuse, or right based on side lengths. It discusses the application of the Triangle Inequality Theorem and provides examples to illustrate these concepts. The video also recaps previous lessons and previews upcoming topics in geometry.

What does the Pythagorean Inequalities Theorem help us classify?

• Types of triangles

• Types of quadrilaterals

• Types of circles

• Types of polygons

If c² > a² + b² in a triangle, what type of triangle is it?

• Obtuse

• Right

• Equilateral

• Acute

What should you do if side lengths are given as a mix of fractions and decimals?

• Convert them to decimals or improper fractions

• Convert them to percentages

• Leave them as they are

• Convert them to whole numbers

According to the hinge theorem, if c² < a² + b², what happens to angle C?

• It becomes 180 degrees

• It remains 90 degrees

• It becomes less than 90 degrees

• It becomes greater than 90 degrees

What does the triangle inequality theorem state?

• The sum of any two side lengths of a triangle is less than the third side length

• The sum of any two side lengths of a triangle is greater than the third side length

• The sum of all side lengths of a triangle is equal to the perimeter

• The sum of all angles in a triangle is 180 degrees

What is a Pythagorean triple?

• A set of three numbers that are all prime

• A set of three angles that add up to 180 degrees

• A set of three nonzero numbers that fit the rule a² + b² = c²

• A set of three sides that form an equilateral triangle

What should you do if side lengths are given in different increments?

• Convert them to percentages

• Convert them to fractions

• Leave them as they are

• Convert them to equivalent units