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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

In the equation a² + b² = c², what does 'c' represent?

Back

'c' represents the length of the hypotenuse, which is the side opposite the right angle and is always the longest side of a right triangle.

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5.

Front

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

Back

In a right triangle, the length of the hypotenuse is always greater than the lengths of either of the other two sides.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem is specifically for right triangles.

Front

What is the formula to find the length of a missing side in a right triangle if the hypotenuse and one side are known?

Back

If the hypotenuse (c) and one side (a) are known, the length of the missing side (b) can be found using the formula: b = √(c² - a²).

Front

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

Back

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

Front

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

Back

The Pythagorean Theorem is used in various real-world applications, such as construction, navigation, and physics, to determine distances and relationships between points.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.