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

If one side of a right triangle is 6 units and the other side is 8 units, what is the length of the hypotenuse?

Back

10 units (using the Pythagorean Theorem: 6² + 8² = c², so 36 + 64 = 100, thus c = 10).

Front

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

Back

The formula is c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

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

How do you calculate the diagonal of a rectangle using the Pythagorean Theorem?

Back

To find the diagonal (d) of a rectangle, use the formula d² = width² + height².

Front

If a rectangular monitor is 30 cm wide and 24 cm high, what is its diagonal size?

Back

38 cm (using the formula: d² = 30² + 24² = 900 + 576 = 1476, thus d = √1476 ≈ 38).

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 that satisfies the Pythagorean Theorem: 3² + 4² = 5².

Front

What is the length of the missing side if one side is 9 and the hypotenuse is 12?

Back

The missing side is 6 (using the Pythagorean Theorem: 12² = 9² + b², so 144 = 81 + b², thus b² = 63, b = √63 ≈ 7.9).

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c² (e.g., 3, 4, 5).