GCSE Secondary Maths Age 13-17 - Algebra: Pythagoras Theorem - Explained

The video tutorial explains how to prove that the area of a square formed by four right-angled triangles is equal to the sum of the squares of the two shorter sides of the triangle. The teacher uses Pythagoras' theorem to demonstrate this, showing that the hypotenuse of the triangle is the side of the square. The tutorial concludes with a discussion on the allocation of marks for the problem, emphasizing the application of Pythagoras' theorem in a unique context.

What is the main objective when arranging four right-angled triangles to form a square ABCD?

• To determine the length of the hypotenuse

• To demonstrate that the area of the square is X^2 + Y^2

• To find the perimeter of the square

• To calculate the volume of the square

Which mathematical theorem is used to relate the sides of the triangle to the hypotenuse in this problem?

• The Triangle Inequality Theorem

• Pythagoras' theorem

• The Law of Sines

• The Law of Cosines

In the context of this problem, what does BC represent?

• The length of one side of the square

• The hypotenuse of the right-angled triangle

• The perimeter of the square

• The diagonal of the square

How many marks are allocated for proving that the area of the square is X^2 + Y^2?

• Two marks

• Four marks

• Three marks

• One mark

What is the significance of using congruent triangles in this problem?

• To prove the triangles are similar

• To demonstrate the equality of the square's sides

• To simplify the calculation of the square's area

• To ensure the triangles have equal perimeters