Pythagorean Theorem: Missing Side

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: a² + b² = c².

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

Which set of sides forms a right triangle? 4, 5, 6 or 5, 12, 13?

Back

5, 12, 13 forms a right triangle.

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

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 the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

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

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

In a 5-12-13 triangle, it is a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

How far is the base of a ladder from the wall if the ladder is 13 m long and reaches 12 m up the wall?

Back

5 m (Using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5).