Exploring the Pythagorean Theorem

This video tutorial covers the Pythagorean Theorem, explaining its formula and application in right-angled triangles. It includes examples of finding the hypotenuse and a leg of a triangle, as well as applying the theorem to 3D shapes like pyramids. The video emphasizes the importance of identifying the hypotenuse and provides practice problems for viewers.

Who is credited with the creation of the Pythagorean theorem?

• Euclid

• Pythagoras

• Albert Einstein

• Isaac Newton

What is the formula of the Pythagorean theorem?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• 2a + 2b = c^2

• a^3 + b^3 = c^3

In a right-angled triangle, what does 'c' represent in the Pythagorean theorem?

• The hypotenuse

• The base

• One of the legs

• The altitude

If one leg of a right-angled triangle is 5 units and the other is 12 units, what is the length of the hypotenuse?

• 12 units

• 13 units

• 14 units

• 11 units

How do you calculate the length of a leg in a right-angled triangle if you know the hypotenuse and the other leg?

• Divide the hypotenuse by the known leg

• Subtract the square of the known leg from the square of the hypotenuse

• Multiply the hypotenuse by the known leg

• Add the squares of the hypotenuse and the known leg

What is the length of a leg if the hypotenuse is 2.9 units and the other leg is 2.1 units?

• 2 units

• 2.5 units

• 3 units

• 3.5 units

Why must the hypotenuse always be the longest side in a right-angled triangle?

• It is the shortest side

• It is opposite the right angle

• It is the base of the triangle

• It is always a perfect square

In the context of a square pyramid, what does the slant height represent?

• The length of the base's diagonal

• The height of the pyramid

• The height from the base to the apex

• The length from the base's center to a vertex along the surface

Using the Pythagorean theorem, how do you find the slant height of a square pyramid?

• Add the squares of the base's side and the pyramid's height

• Add the squares of half the base and the height

• Square the height and subtract it from the square of the base

• Square the base and add it to the square of the height

If the sides of the base of a square pyramid are 6.4 units and 4.8 units, what is the slant height?

• 9 units

• 8 units

• 10 units

• 7 units