U5 CW #5: The Pythagorean Theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the formula to find the length of a missing side in a right triangle?

Back

c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

When do we use the Pythagorean Theorem?

Back

To find the missing length of a right triangle.

Front

What is the length of the hypotenuse if the legs are 6 and 8?

Back

10 (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100; √100 = 10).

Front

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

Back

In a right triangle, the hypotenuse is always the longest side.

Front

If a right triangle has a hypotenuse of 15 and one leg of 9, what is the length of the other leg?

Back

12 (Using the Pythagorean Theorem: 15² = 9² + b²; 225 = 81 + b²; b² = 144; b = 12).

Front

What is the distance across a rectangular field that is 30 yards wide and 40 yards long?

Back

50 yards (Using the Pythagorean Theorem: 30² + 40² = 900 + 1600 = 2500; √2500 = 50).

Front

What is the Pythagorean Theorem used for in real life?

Back

It is used in various applications such as construction, navigation, and physics to determine distances and angles.