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 are the legs of a right triangle?

Back

The legs of a right triangle are the two shorter sides that form the right angle.

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

If you know the lengths of the legs of a right triangle, how do you find the distance between two points represented by these legs?

Back

Use the Pythagorean Theorem to calculate the hypotenuse, which represents the distance between the two points.

Front

What is the formula to calculate the distance between two points (x1, y1) and (x2, y2) in a coordinate plane?

Back

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

Front

In the context of the Pythagorean Theorem, what does the term 'hypotenuse' refer to?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the relationship between the sides of a right triangle when one side is missing?

Back

If one side is missing, you can use the Pythagorean Theorem to find it by rearranging the formula: a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

The Pythagorean Theorem is used in various fields such as architecture, engineering, and navigation to calculate distances and design structures.

Front

How can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side: a² + b² = c².

Front

What is the approximate distance Lisa drives from her starting point if she goes 46 km south and 13 km east?

Back

Using the Pythagorean Theorem, the distance is approximately 47.8 km.