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 is a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the 'legs' (the two shorter sides) and the 'hypotenuse' (the longest side opposite the right angle).

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: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 cm.

Front

What is the distance from the base of the house to the base of the ladder if the ladder is 13 m long and it reaches 12 m high?

Back

Using the Pythagorean Theorem: c² = a² + b²; 13² = 12² + b²; 169 = 144 + b²; b² = 25; b = 5 m.

Front

Which set of sides forms a right triangle?

Back

The set of sides 5, 12, 13 forms a right triangle because 5² + 12² = 13².

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean Theorem: c² = a² + b², and solve for the unknown side.

Front

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

Back

Using the Pythagorean Theorem: 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8 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.