Pythagoream Theorem Practice - AMCMS 2

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

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

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5 cm.

Front

Do the lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

What is the distance formula used for finding the distance between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the perimeter of a triangle with legs measuring 3 cm and 4 cm?

Back

The perimeter is the sum of all sides. For a right triangle, the third side (hypotenuse) is 5 cm. So, perimeter = 3 + 4 + 5 = 12 cm.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the legs of a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If the hypotenuse is 10 cm and one leg is 6 cm, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + 6² = 10²; a² + 36 = 100; a² = 64; a = 8 cm.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.