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 is expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

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

Which set of sides forms a right triangle? 4, 5, 6 or 5, 12, 13?

Back

5, 12, 13 forms a right triangle.

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

The distance is 5 units (Using the distance formula: √((x2 - x1)² + (y2 - y1)²)).

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

What is the length of the diagonal of a rectangle that is 3 feet tall and 6 feet wide?

Back

6.7 feet (Using the Pythagorean Theorem: 3² + 6² = 9 + 36 = 45; √45 ≈ 6.7).

Front

What is the formula for calculating the hypotenuse in a right triangle?

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has legs of length 5 cm and 12 cm, what is the length of the hypotenuse?

Back

13 cm (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).