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: a² + b² = c².

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the Hypotenuse.

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

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 cm.

Front

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

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

How do you find the diagonal length of a rectangle?

Back

To find the diagonal length of a rectangle, use the formula: d = √(width² + height²).

Front

What is the diagonal length of a rectangle that is 6 cm wide and 8 cm high?

Back

Using the formula: d = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Front

What is a right triangle?

Back

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

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

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

Back

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

Front

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

Back

In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem.