4B Review (Pythagorean Thm)-P4

Front

What is the Pythagorean Theorem?

Back

In a right-angled 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). Formula: c² = a² + b².

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

If a triangle has sides measuring 6 cm, 8 cm, and 10 cm, is it a right triangle?

Back

Yes, it is a right triangle because 10² = 6² + 8² (100 = 36 + 64).

Front

Calculate the length of the diagonal of a square with sides of 5 feet.

Back

The diagonal d can be calculated using the formula d = √(a² + a²) = √(5² + 5²) = √(50) ≈ 7.07 feet.

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

Back

Using the Pythagorean theorem: c² = 3² + 4²; c² = 9 + 16; c = √25 = 5 cm.

Front

What does it mean for a triangle to be a right triangle?

Back

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

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pythagorean Theorem).

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 13² = 5² + 12² (169 = 25 + 144).

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) × base × height.