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

How do you identify the hypotenuse in a right triangle?

Back

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

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², depending on which side is missing.

Front

If one side of a right triangle is 14 and the hypotenuse is 20, what is the length of the other side?

Back

Using the Pythagorean Theorem: b² = c² - a²; b² = 20² - 14²; b² = 400 - 196; b² = 204; b = √204 ≈ 14.4.

Front

What is the approximate value of the square root of 20?

Back

The approximate value of the square root of 20 is about 4.5.

Front

How do you estimate the square root of a number?

Back

To estimate the square root, find two perfect squares between which the number lies and then approximate based on their square roots.

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 the ratio of 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²).

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Front

How can the Pythagorean Theorem be applied to find distances in coordinate geometry?

Back

In coordinate geometry, the distance between two points (x₁, y₁) and (x₂, y₂) can be found using the formula: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

What is the value of the hypotenuse if the two other sides of a right triangle are 6 and 8?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.