Exploring the Pythagorean Theorem

The video tutorial introduces the Pythagorean theorem, explaining its application to right triangles. It details how to identify the sides of a triangle, specifically the legs and hypotenuse, and demonstrates how to use the theorem to find missing side lengths. The tutorial includes several example problems to illustrate the process, emphasizing the importance of the hypotenuse being the longest side. The video also provides guidance on using a calculator to find square roots, ensuring students can solve problems accurately.

What type of triangles does the Pythagorean theorem apply to?

• Scalene triangles

• Right triangles

• Isosceles triangles

• Equilateral triangles

What is the correct formula for the Pythagorean theorem?

• a + b = c^2

• a^2 * b^2 = c^2

• a^2 + b^2 = c

• a^2 + b^2 = c^2

If one leg of a right triangle is 11 units and the other is 12 units, what is the length of the hypotenuse?

• 16.27 units

• 23 units

• 5.5 units

• 10 units

Can the labels 'a' and 'b' for the legs of a right triangle be interchanged without affecting the outcome?

• Yes, they are interchangeable

• No, 'a' must always be the shorter leg

• No, 'b' must always be the longer leg

• Yes, but only if 'c' is also relabeled

What is the purpose of taking the square root in the Pythagorean theorem?

• To determine the length of the hypotenuse

• To find the area of the triangle

• To calculate the perimeter of the triangle

• To establish the height of the triangle

In a right triangle, if the lengths of the legs are 4 units and 6 units, what is the length of the hypotenuse?

• 5 units

• 10 units

• 8 units

• 7.21 units

For a right triangle with legs of 13 units and 7 units, how long is the hypotenuse?

• 15 units

• 20.76 units

• 14.76 units

• 10 units

What is the result of applying the Pythagorean theorem to a triangle with legs 5 units and 7 units?

• 8.60 units

• 12 units

• 6.40 units

• 9.22 units

Using the Pythagorean theorem, what is the hypotenuse of a triangle with sides 10 units and 11 units?

• 13.45 units

• 15.81 units

• 14.86 units

• 21.22 units

If a right triangle has legs of 9 units and 3 units, what is the length of the hypotenuse?

• 10.50 units

• 11.40 units

• 12 units

• 9.49 units