Expressing Geometric Properties with Equations (G.GPE)

Front

What is the definition of parallel lines in geometry?

Back

Parallel lines are lines in a plane that do not intersect or touch each other at any point, no matter how far they are extended.

Front

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

Back

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

Front

What is the formula for the area of a square?

Back

The area A of a square is given by the formula: A = side², where 'side' is the length of one side of the square.

Front

What is the definition of the radius of a circle?

Back

The radius of a circle is the distance from the center of the circle to any point on its circumference.

Front

How do you calculate the area of a triangle?

Back

The area A of a triangle can be calculated using the formula: A = 1/2 * base * height.

Front

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

Back

The midpoint M is calculated as: M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the definition of an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.

Front

How do you determine if a point lies on a circle given its center and radius?

Back

A point (x, y) lies on a circle with center (h, k) and radius r if: (x - h)² + (y - k)² = r².

Front

What is the distance formula derived from the Pythagorean theorem?

Back

The distance formula is derived from the Pythagorean theorem and is used to find the distance between two points in a plane.

Front

What is the definition of a square in geometry?

Back

A square is a quadrilateral with four equal sides and four right angles.