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 is a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

5 cm (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

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

How do you find the length of a side if you know the hypotenuse and one other side?

Back

Rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², then take the square root to find the length.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the sides are in a ratio of 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²).

Front

If the hypotenuse of a right triangle is 10 cm and one side is 6 cm, what is the length of the other side?

Back

8 cm (Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8).

Front

What is the area of a right triangle with a base of 5 cm and a height of 12 cm?

Back

30 cm² (Area = 1/2 * base * height = 1/2 * 5 * 12).

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.