Apply the Area of Squares Proof to determine if a triangle is a right triangle

This video tutorial teaches how to determine if a triangle is a right triangle using the area of squares proof and the Pythagorean theorem. It explains the relationship between the areas of squares formed by the sides of a triangle and how to verify if a triangle is right-angled. The tutorial includes examples of constructing triangles with squares and addresses common misconceptions about right triangles.

What is the relationship between the squares of the sides of a right triangle?

• The squares of the legs are greater than the square of the hypotenuse.

• The square of the hypotenuse is less than the sum of the squares of the legs.

• The sum of the squares of all sides is equal.

• The sum of the squares of the legs equals the square of the hypotenuse.

What type of triangle is formed when three squares with equal areas are combined?

• Right triangle

• Equilateral triangle

• Isosceles triangle

• Scalene triangle

Which of the following sets of side lengths can form a right triangle?

• 3, 4, 5

• 6, 7, 8

• 2, 3, 4

• 5, 5, 5

If a triangle has side lengths of 6, 6, and 9, does it form a right triangle?

• Yes, because 6 + 6 equals 9

• Yes, because it looks like a right triangle

• No, because 6 and 9 are not equal

• No, because 36 + 36 does not equal 81

What is a common misunderstanding about right triangles?

• Right triangles have no hypotenuse

• All triangles are right triangles

• Right triangles have equal sides

• Any triangle that looks like a right triangle is one

Which of the following side lengths does not form a right triangle?

• 6, 8, 10

• 5, 12, 13

• 7, 24, 25

• 2, 8, 12

How can you verify if a triangle is a right triangle using side lengths?

• Check if all sides are equal

• Check if the sum of the squares of the two shorter sides equals the square of the longest side

• Check if the triangle has a 90-degree angle

• Check if the sum of all sides is even