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). Formula: a² + b² = c².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, 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

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the perimeter of a right triangle with legs of 3 cm and 4 cm?

Back

12 cm (Perimeter = a + b + c = 3 + 4 + 5).

Front

What does it mean to square a number?

Back

To square a number means to multiply the number by itself.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

In the Pythagorean Theorem, what do 'a' and 'b' represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of a right triangle.

Front

What is the relationship between the areas of the squares on the sides of a right triangle?

Back

The sum of the areas of the two smaller squares (on sides a and b) is equal to the area of the larger square (on side c).

Front

Is the statement 'Side a is always the longest side' true or false?

Back

False. The longest side in a right triangle is the hypotenuse, which is usually denoted as 'c'.

Front

If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle?

Back

Yes, it is a right triangle (5² + 12² = 25 + 144 = 169; √169 = 13).