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hOORAY4@ngles!

GEOMETRY

The circumference of a circle is                       2 * π * r

The diameter of a circle is                            2 * r

The area of a circle is                                    2 * π * r²

C = 2πr

D = 2r

A = πr²

Rectangular shape

volume = length * width * height

Points, Lines, and Planes:

  • A point is a location in space.

  • A line is a straight path that extends infinitely in both directions.

  • A plane is a flat surface that extends infinitely in all directions.

NEED TO KNOW

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Angles:

  • An angle is formed by two rays with a common endpoint (vertex).

  • Types of angles include:

    • Acute Angle: Less than 90 degrees.

    • Right Angle: Exactly 90 degrees.

    • Obtuse Angle: More than 90 degrees but less than 180 degrees.

    • Straight Angle: Exactly 180 degrees.

    • Reflex Angle: More than 180 degrees but less than 360 degrees.

Triangles:

  • A triangle is a polygon with three sides.

  • Types of triangles include:

    • Equilateral: All sides are of equal length.

    • Isosceles: Two sides are of equal length.

    • Scalene: No sides are of equal length.

    • Right Triangle: One angle is exactly 90 degrees.

Quadrilaterals:

  • A quadrilateral is a polygon with four sides.

  • Types of quadrilaterals include:

    • Square: All sides are of equal length and angles are right angles.

    • Rectangle: Opposite sides are of equal length and angles are right angles.

    • Rhombus: All sides are of equal length.

    • Parallelogram: Opposite sides are parallel and equal in length.

Circles:

  • A circle is a set of all points in a plane that are equidistant from a given point called the center.

  • Key terms:

    • Radius: Distance from the center to any point on the circle.

    • Diameter: Twice the radius.

    • Circumference: The perimeter of a circle (2 * π * radius).

    • Area: π * radius².

Area and Perimeter:

  • Area is the measure of the space inside a shape.

  • Perimeter is the total length of the sides of a shape.

  • Formulas for common shapes:

    • Rectangle:

      • Area = length * width

      • Perimeter = 2 * (length + width)

    • Triangle:

      • Area = (base * height) / 2

    • Circle:

      • Area = π * radius²

      • Circumference = 2 * π * radius

Volume:

  • Volume is the amount of space enclosed by a 3D shape

  • Formulas for common solids:

    • Cube: Volume = side³

    • Cylinder: Volume = π * radius² * height

    • Sphere: Volume = (4/3) * π * radius³

Transformations:

  • Translation: Sliding a shape without changing its size or shape.

  • Rotation: Turning a shape around a fixed point.

  • Reflection: Flipping a shape over a line.

Similarity and Congruence:

  • Similar Figures: Have the same shape but not necessarily the same size.

  • Congruent Figures: Have the same shape and the same size.

Coordinate Geometry:

  • Coordinate Plane: A grid formed by an x-axis and a y-axis.

  • Distance Formula: Used to find the distance between two points.

  • Slope Formula: Used to find the slope of a line.

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