December 4, 24 Flashcardziz Review Pythagorean Thm.

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

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the lengths of the sides must satisfy the Pythagorean Theorem. If the lengths do not satisfy a² + b² = c², then the triangle is not a right triangle.

Front

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

Back

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

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The diagonal (d) of a rectangle can be calculated using the formula: d = √(length² + width²).

Front

Which of the following sets of lengths can represent the sides of a right triangle: 6 cm, 8 cm, 10 cm or 4 cm, 6 cm, 10 cm?

Back

The set 6 cm, 8 cm, 10 cm can represent the sides of a right triangle because 6² + 8² = 10² (36 + 64 = 100). The set 4 cm, 6 cm, 10 cm cannot represent the sides of a right triangle because 4² + 6² ≠ 10² (16 + 36 ≠ 100).

Front

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

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean Theorem.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the lengths of the sides satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

What is the height of a right triangle if the base is 6 feet and the hypotenuse is 10 feet?

Back

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

Front

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

Back

Using the Pythagorean Theorem: b = √(13² - 5²) = √(169 - 25) = √144 = 12.