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 ONLY works on right triangles.

Front

If one side of a right triangle is 3 cm and the other side 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

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

In a right triangle, if the lengths of the legs are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

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

Front

Which set of sides can form a right triangle? 6, 8, 10 or 5, 10, 12 or 7, 24, 25?

Back

The set 6, 8, 10 can form a right triangle because 6² + 8² = 10² (36 + 64 = 100).

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

Back

Using the Pythagorean Theorem: 9² + b² = 15²; 81 + b² = 225; b² = 144; b = 12 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.