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

What is a right triangle?

Back

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

Front

How do you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the Pythagorean Theorem holds true: a² + b² = c², where c is the longest side.

Front

What is the distance formula?

Back

The distance formula is used to find 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 M of a line segment with endpoints (x1, y1) and (x2, y2). It is given by: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

If one endpoint of a segment is (2, 3) and the midpoint is (6, 7), what is the other endpoint?

Back

The other endpoint is (10, 11).

Front

If one endpoint of a segment is (5, -2) and the midpoint is (8, 1), what is the other endpoint?

Back

The other endpoint is (11, 4).

Front

Calculate the distance between the points (1, 2) and (4, 6).

Back

The distance is 5 units.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Front

How can you find the length of one side of a right triangle if the other two sides are known?

Back

You can use the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the other sides.