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 is expressed as: c² = a² + b².

Front

What does 'c' represent in the Pythagorean Theorem?

Back

'c' represents the length of the hypotenuse, which is the side opposite the right angle in a right triangle.

Front

What do 'a' and 'b' represent in the Pythagorean Theorem?

Back

'a' and 'b' represent the lengths of the two legs (the sides that form the right angle) of a right triangle.

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 = 9 + 16 = 25. Therefore, c = √25 = 5 cm.

Front

Which of the following sets of numbers can represent the sides of a right triangle? 5, 12, 13 or 8, 10, 12?

Back

5, 12, 13 can represent the sides of a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True. The Pythagorean Theorem is specifically applicable to right triangles.

Front

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

Back

To find the length of a missing side, use the formula: c² = a² + b², where c is the hypotenuse and a and b are the legs.

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: 10² = 6² + b². Therefore, 100 = 36 + b², so b² = 64, and 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.