Exploring the Converse of the Pythagorean Theorem

This video lesson covers the converse of the Pythagorean theorem, starting with a warm-up on identifying the hypotenuse in right triangles. It explains the triangle inequality theorem, which helps determine if three numbers can form a triangle. The lesson then focuses on the converse of the Pythagorean theorem, which is used to classify triangles as right, acute, or obtuse based on side lengths. Several examples and practice problems are provided to reinforce these concepts.

Which side of a triangle is always the longest?

• The altitude

• The base

• The hypotenuse

• The median

What theorem helps determine if three numbers can form a triangle?

• Triangle Inequality Theorem

• Pythagorean Theorem

• Sine Rule

• Converse of the Pythagorean Theorem

If the sum of the squares of two sides of a triangle equals the square of the third side, what type of triangle is it?

• Equilateral triangle

• Right triangle

• Obtuse triangle

• Acute triangle

If c^2 > a^2 + b^2, the triangle is:

• Obtuse

• Right

• Isosceles

• Acute

What does it mean if c^2 < a^2 + b^2 in a triangle?

• The triangle is right

• The triangle is equilateral

• The triangle is obtuse

• The triangle is acute

Which theorem is used to classify triangles as acute, obtuse, or right based on their side lengths?

• Triangle Inequality Theorem

• Converse of the Triangle Inequality Theorem

• Sine Rule

• Converse of the Pythagorean Theorem

For a triangle with sides 5, 7, and 10, what type of triangle is it?

• Obtuse

• Right

• Equilateral

• Acute

If a triangle's side lengths are 7, 12, and 16, what type of triangle is it?

• Acute

• Right

• Isosceles

• Obtuse

Which condition immediately indicates that three lengths cannot form a triangle?

• All sides are of equal length

• The sum of any two sides is less than the third side

• The longest side is less than the sum of the other two

• The sum of any two sides equals the third side

In a triangle with sides 5.2, 12, and 13, what type of triangle is it?

• Right

• Obtuse

• Acute

• Equilateral