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 applies to right triangles.

Front

In a right triangle, what are the sides called?

Back

The two sides that form the right angle are called the legs, and the side opposite the right angle is called the hypotenuse.

Front

If one leg of a right triangle is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 cm.

Front

What is the distance between two points (3, 4) and (0, 0) in a coordinate plane?

Back

Using the distance formula derived from the Pythagorean Theorem: d = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5.

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) can be found using the Pythagorean Theorem: d = √(length² + width²).

Front

If a right triangle has legs of lengths 9 cm and 12 cm, what is the length of the hypotenuse?

Back

c² = 9² + 12²; c² = 81 + 144; c² = 225; c = 15 cm.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do 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 a² + b² = c² holds true for the lengths of the sides.