Unit 6 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 can be expressed as: a² + b² = c².

Front

What is the formula to find the area of a square?

Back

The area of a square is calculated by squaring the length of one of its sides. The formula is: Area = side².

Front

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

Back

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

Front

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

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Front

What is the length of the hypotenuse if one leg is 6 units and the other leg is 8 units?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10 units.

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

How do you find the length of one leg of a right triangle if you know the hypotenuse and the other leg?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

Front

What is the height of a TV screen if the diagonal measurement is 40 inches and the width is 31.2 inches?

Back

Using the Pythagorean Theorem: height² = diagonal² - width² = 40² - 31.2² = 1600 - 973.44 = 626.56. Therefore, height = √626.56 ≈ 25.0 inches.

Front

What is the area of a square with a side length of 13 units?

Back

Area = side² = 13² = 169 square units.

Front

If a ladder is 15 feet long and the foot of the ladder is 9 feet away from the wall, how high does it reach on the wall?

Back

Using the Pythagorean Theorem: height² = ladder² - distance² = 15² - 9² = 225 - 81 = 144. Therefore, height = √144 = 12 feet.