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 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 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

What is the formula to find the area of a square?

Back

The area of a square is found by squaring the length of one of its sides: Area = side².

Front

If the area of a square is 36 in², what is the length of one side?

Back

6 in (since √36 = 6).

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

How do you find the distance between two points on a coordinate plane?

Back

Use the distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

What is the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

If the base of a triangle is 10 cm and the height is 5 cm, what is the area?

Back

25 cm² (Area = 1/2 * 10 * 5 = 25).