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 is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side 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 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

How do you find the length of a diagonal in a rectangle?

Back

To find the length of the diagonal in a rectangle, use the Pythagorean Theorem: d² = length² + width², where d is the diagonal.

Front

If a rectangular field is 30 yards wide and 40 yards long, how long is the diagonal?

Back

50 yards (Using the Pythagorean Theorem: 30² + 40² = 900 + 1600 = 2500; √2500 = 50).

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in a ratio that satisfies the Pythagorean Theorem: 3² + 4² = 5².

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and computer graphics, to calculate distances and create right angles.

Front

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

Back

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