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: a² + b² = c².

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 the Pythagorean Theorem, which side is represented by 'c'?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse.

Front

If a right triangle has sides of length 3 and 4, what is the length of the hypotenuse?

Back

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

Front

Can a triangle with sides of lengths 2, 3, and 4 be a right triangle?

Back

No, because 2² + 3² = 4 + 9 = 13, which is not equal to 4² (16).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.

Front

If one side of a right triangle is 5 and the hypotenuse is 13, what is the length of the other side?

Back

Using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

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

Front

What does it mean for lengths to form a right triangle?

Back

Lengths form a right triangle if they satisfy the Pythagorean Theorem: a² + b² = c².