Pythagorean theorem Review

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

Back

To find the length of the diagonal (d) of a rectangle, use the formula: d = √(width² + length²).

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

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

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. The side opposite the 30° angle is the shortest.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

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

Back

To find the distance (d) between two points (x1, y1) and (x2, y2), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the length of the hypotenuse if both legs of a right triangle are 6 cm?

Back

Using the Pythagorean Theorem: c = √(6² + 6²) = √(36 + 36) = √72 = 6√2 cm.

Front

What is the area of a right triangle with a base of 5 cm and a height of 12 cm?

Back

The area (A) of a right triangle is given by A = (1/2) × base × height. So, A = (1/2) × 5 × 12 = 30 cm².

Front

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

Back

Using the Pythagorean Theorem: b = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and computer graphics to calculate distances and create right angles.