Understanding Pythagoras' Theorem

The video tutorial introduces Pythagoras' theorem using an analogy of gold squares. It explains that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The video demonstrates how to apply the theorem through example problems, showing how to calculate unknown side lengths. It concludes by summarizing the key points and emphasizing the theorem's application to right-angled triangles.

What is the surprising fact about the two smaller squares compared to the larger square?

• They are larger than the big square.

• They are made of different materials.

• They are the same size as the large square.

• They are heavier than the large square.

What is Pythagoras' theorem primarily used for?

• Determining the length of a side in a right-angled triangle.

• Calculating the volume of a cube.

• Finding the area of a circle.

• Measuring the perimeter of a rectangle.

In the example, what is the length of the hypotenuse when the other sides are 4 and 3?

• 7

• 5

• 6

• 8

What is the first step in solving for the hypotenuse using Pythagoras' theorem?

• Divide the sides by two.

• Add the squares of the two shorter sides.

• Multiply the sides together.

• Subtract the squares of the sides.

What is the length of the side found in the second example problem?

• 5 kilometers

• 4 kilometers

• 6 kilometers

• 3 kilometers

How do you rearrange Pythagoras' theorem to find a shorter side?

• Add the squares of the sides.

• Multiply the squares of the sides.

• Divide the hypotenuse by the shorter side.

• Subtract the square of the known shorter side from the square of the hypotenuse.

What is the key condition for using Pythagoras' theorem?

• The triangle must be equilateral.

• The triangle must be right-angled.

• The triangle must be isosceles.

• The triangle must be scalene.

What do the squares of the smaller sides add up to in a right-angled triangle?

• The square of the hypotenuse.

• The sum of the angles.

• The perimeter of the triangle.

• The area of the triangle.

If you know the hypotenuse and one side, how do you find the other side?

• Divide the hypotenuse by the known side.

• Multiply the sides together.

• Subtract the square of the known side from the square of the hypotenuse.

• Add the squares of the sides.

What is the result when you square the hypotenuse and subtract the square of one side?

• The sum of the angles.

• The square of the other side.

• The perimeter of the triangle.

• The area of the triangle.