Pythagorean Theorem, Distance, and Midpoint

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

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. Rearrange the formula a² + b² = c² to solve for the missing side.

Front

What is the distance formula?

Back

The distance formula is used to determine the distance between two points (x1, y1) and (x2, y2) in a coordinate plane. It is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the midpoint formula?

Back

The midpoint formula is used to find the midpoint of a line segment between two points (x1, y1) and (x2, y2). It is given by: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem: a² + b² = c², where c is the length of the hypotenuse.

Front

If one side of a right triangle is 5 cm and the other is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13 cm.

Front

What is the length of the hypotenuse if the two other sides are 8 in. and 15 in.?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17 in.

Front

Find 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 endpoint of a segment if one endpoint is (2, 3) and the midpoint is (4, 5)?

Back

Using the midpoint formula, if (x1, y1) is (2, 3) and midpoint is (4, 5), then the other endpoint (x2, y2) can be found as follows: x2 = 2*4 - 2 = 6, y2 = 2*5 - 3 = 7. So, the endpoint is (6, 7).

Front

Which set of sides can form a right triangle: 6, 8, 10 or 7, 24, 25?

Back

Both sets can form a right triangle. For 6, 8, 10: 6² + 8² = 36 + 64 = 100 = 10². For 7, 24, 25: 7² + 24² = 49 + 576 = 625 = 25².