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

If a = 3 and b = 4, what is c?

Back

c = 5 (Using the Pythagorean Theorem: 3² + 4² = c² => 9 + 16 = c² => c² = 25 => c = 5).

Front

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

Back

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

Front

If c = 10 and a = 6, what is b?

Back

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

Front

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

Back

True.

Front

What is the length of the hypotenuse if the other two sides are 5 cm and 12 cm?

Back

The hypotenuse is 13 cm (5² + 12² = c² => 25 + 144 = c² => c² = 169 => c = 13).

Front

If a = 8 and c = 10, what is b?

Back

b = 6 (Using the Pythagorean Theorem: 10² = 8² + b² => 100 = 64 + b² => b² = 36 => b = 6).

Front

What does 'hypotenuse' mean?

Back

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

Front

If a = 7 and b = 24, what is c?

Back

c = 25 (Using the Pythagorean Theorem: 7² + 24² = c² => 49 + 576 = c² => c² = 625 => c = 25).

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two shorter sides (a and b) equals the square of the longest side (c): a² + b² = c².