Pythagorean Theorem (5.5)

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 legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

What is the hypotenuse of 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

How do you determine if a set of three lengths can form a right triangle?

Back

Use the Pythagorean Theorem: Check if a² + b² = c², where c is the longest side.

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

Back

6 cm² (Area = 1/2 * base * height = 1/2 * 3 * 4).

Front

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

Back

It is a Pythagorean triple, meaning it satisfies the Pythagorean Theorem: 5² + 12² = 13².

Front

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

Back

8 cm (Using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64; √64 = 8).