Pythagorean Theorem (Finding the Hypotenuse)

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 side of a right triangle is 5 cm and the other side is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13 cm.

Front

What is the formula to find the hypotenuse using the Pythagorean Theorem?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

Calculate the hypotenuse if the two other sides are 8 cm and 15 cm.

Back

c = √(8² + 15²) = √(64 + 225) = √289 = 17 cm.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If the hypotenuse is 10 cm and one side is 6 cm, how do you find the other side?

Back

Use the formula: b = √(c² - a²); b = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, is it a right triangle?

Back

Yes, because 25² = 7² + 24² (625 = 49 + 576).

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.