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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 15 and the hypotenuse is 21, what is the length of the other side?

Back

Using the Pythagorean Theorem: 15² + x² = 21². Solving gives x = 12.

Front

What is the formula to find the distance between two points (x1, y1) and (x2, y2)?

Back

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

Front

Calculate the distance between the points (3, 4) and (7, 1).

Back

Using the distance formula: d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Front

What is the value of x in the equation 15² + x² = 21²?

Back

x = √(21² - 15²) = √(441 - 225) = √216 = 14.7.

Front

What is 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 according to the Pythagorean Theorem?

Back

The sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

If a right triangle has legs of lengths 8 and 6, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 8² + 6² = c²; 64 + 36 = c²; c² = 100; c = 10.

Front

What is the hypotenuse of a right triangle with legs measuring 9 and 12?

Back

Using the Pythagorean Theorem: 9² + 12² = c²; 81 + 144 = c²; c² = 225; c = 15.