Pythagorean Theorem Flashcard Review

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 is expressed as a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

In the equation a² + b² = c², what do a and b represent?

Back

In the equation a² + b² = c², a and b represent the lengths of the two legs (the sides that form the right angle) of a right triangle.

Front

What does side c represent in a right triangle?

Back

Side c represents the length of the hypotenuse, which is the side opposite the right angle and is always the longest side in a right triangle.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.

Front

How do you find the length of one side of a right triangle if you know the lengths of the other two sides?

Back

You can rearrange the Pythagorean Theorem: if you know a and b, you can find c using c = √(a² + b²). If you know c and one leg, you can find the other leg using a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

In a right triangle, the length of the hypotenuse is always greater than the lengths of either leg.

Front

What is the approximate distance Patrick walks diagonally across a rectangular field that is 50 yards wide and 100 yards long?

Back

Using the Pythagorean Theorem: c = √(50² + 100²) = √(2500 + 10000) = √12500 ≈ 111.8 yards.

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

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

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.