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 the hypotenuse in a right triangle?

Back

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

Front

If one leg of a right triangle is 3 cm and the other leg 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

How do you find the length of a missing side using the Pythagorean Theorem?

Back

To find a missing side, rearrange the formula: c² = a² + b². If you know two sides, you can solve for the third.

Front

What is the formula for the Pythagorean Theorem?

Back

c² = a² + b².

Front

In a right triangle, if the legs are 5 cm and 12 cm, what is the hypotenuse?

Back

13 cm (5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What do you do to both sides of the equation to solve for a side in the Pythagorean Theorem?

Back

You take the square root of both sides.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

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

Back

Use the formula: b² = c² - a². Here, b² = 10² - 6² = 100 - 36 = 64; b = √64 = 8 cm.

Front

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

Back

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