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: c² = a² + b².

Front

What does the hypotenuse represent in a right triangle?

Back

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

Front

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

Back

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

Front

If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

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

Front

True or False: The legs of a right triangle are always equal in length.

Back

False. The legs can be of different lengths.

Front

What is the relationship between the areas of squares constructed on the legs and the hypotenuse of a right triangle?

Back

The area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Front

If a right triangle has a hypotenuse of 10 units and one leg of 6 units, what is the length of the other leg?

Back

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

Front

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

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

What is the significance of the right angle in a right triangle?

Back

The right angle (90 degrees) is the angle that defines a right triangle and is essential for applying the Pythagorean Theorem.

Front

If the lengths of the legs of a right triangle are both 5 units, what is the length of the hypotenuse?

Back

√(5² + 5²) = √(25 + 25) = √50 ≈ 7.07 units.