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 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

What is the hypotenuse of 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 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 cm.

Front

What is the distance between two points in a coordinate plane?

Back

The distance can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Front

Can the lengths 4 cm, 6 cm, and 10 cm form a right triangle?

Back

No, they cannot form a right triangle because 4² + 6² = 16 + 36 = 52, which is not equal to 10² (100).

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) can be found using the formula: d = √(length² + width²).

Front

If a rectangular piece of paper measures 8.5 inches by 11 inches, what is the length of the diagonal?

Back

Using the formula: d = √(8.5² + 11²); d = √(72.25 + 121); d = √193.25 ≈ 13.9 inches.