Pythagorean Theorem and Distance Formula 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: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

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

Back

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

Front

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

Back

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

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Front

What is the opposite operation of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

In the context of the Pythagorean Theorem, what do 'a' and 'b' represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs of a right triangle.

Front

If a rectangular field is 30 yards wide and 40 yards long, how far is it diagonally across?

Back

Using the Pythagorean Theorem: c² = 30² + 40²; c² = 900 + 1600; c² = 2500; c = 50 yards.

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the value of c if a = 5 and b = 12 in a right triangle?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.