Pythagorean Theorem

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 are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

Do the segment lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

Which set of sides would make a right triangle? 4,5,6; 8,10,12; 5,12,13; 5,10,12

Back

5, 12, 13, because 5² + 12² = 13² (25 + 144 = 169).

Front

How do you find the distance between two points (x1, y1) and (x2, y2)?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the relationship between the areas of the squares on the sides of a right triangle?

Back

The sum of the areas of the two smaller squares is equal to the area of the large square (the square on the hypotenuse).

Front

If a computer monitor is 27 inches diagonally and 15 inches in height, how do you find the width?

Back

Use the Pythagorean Theorem: width = √(27² - 15²) = √(729 - 225) = √504 ≈ 22 inches.

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the side opposite the right angle and is the longest side of the triangle.

Front

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

Back

Area = side².