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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 5 cm and the other side is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13 cm.

Front

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

Back

The formula is c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

In a right triangle, if one leg is 9 cm and the hypotenuse is 15 cm, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² = c² - b²; a² = 15² - 9²; a² = 225 - 81; a² = 144; a = 12 cm.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5² (9 + 16 = 25).

Front

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

Back

Using the Pythagorean Theorem: b² = c² - a²; b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8 cm.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is d = √((x2 - x1)² + (y2 - y1)²), which calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane.

Front

How can the Pythagorean Theorem be used in real-life situations?

Back

The Pythagorean Theorem can be used in various real-life situations such as construction, navigation, and determining distances.

Front

What is the value of c in a right triangle with sides of length 8 cm and 15 cm?

Back

Using the Pythagorean Theorem: c² = 8² + 15²; c² = 64 + 225; c² = 289; c = 17 cm.