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Math Study Lounge
These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.
    - Getting Started with Algebra
    - Geometry Basics
    - How to Solve Math Problems
    - Trigonometry Quick Review
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Home » Geometry Basics

Key Geometry Terms

  • Angle - either the figure formed by two rays starting from a common point or the measure of such a figure. 
  • Complimentary Angles - a pair of angles whose sum is 90˚.
  • Supplementary Angles - a pair of angles whose sum is 180˚.
  • Congruent Angles - angles with the same angle measurement.
  • Vertical Angles - angles at an intersection of two lines that are not adjacent to each other.
  • Interior Angles - pair of angles that are in the interior of a polygon, OR angles inside or between two parallel lines.
  • Exterior Angles - pair of angles formed by the side of a polygon and an adjacent, extended side OR angles on the outside of two parallel lines.
  • Circle - a figure in which all points are the same distance from the center, that distance being known as the radius.
  • Pi - ratio of the circumference to the diameter of a circle.  Pi is denoted by the Greek symbol “π” and is approximately 3.14159, though it is widely known to continue to an infinite number of decimals and thus, is irrational.
  • Pythagorean Theorem - the sum of the squares for the legs of a right triangle equal the square of the hypotenuse
  • Special Right Triangles - right triangles where certain relationships always hold true.  These relationships, when recognized, are useful since they reduce sometimes complex work to solving a proportion or even mental math.
  • Regular polygon - a geometric figure with three or more sides in which all interior angles are congruent.
  • Area - size of a planar region or surface of a solid.  Areas are measured in “square” units.
  • Volume - amount of space taken up by or enclosed by an object.  Volumes are measured in “cubic” units.
  • Degree - unit of angle measurement equal to 1/360 of a circle’s circumference.
  • Radian - unit of angle measurement that is the ratio ofthe circle arc cut off by an angle to the central angle.
  • Sine - on a unit circle, the “y” coordinate for any intersection between a standard angle and the circle.  In a right triangle, the ratio of the length of the opposite side to the length of the hypotenuse.
  • Cosine - on a unit circle, the “x” coordinate for any intersection between a standard angle and the circle.  In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.
  • Tangent - the ratio of sine to cosine or, in a right triangle, the ratio of the length of the opposite side to the length of the adjacent side.
  • Secant - reciprocal of cosine (sec θ = 1 / cos θ).
  • Cosecant - reciprocal of sine (csc θ = 1 / sin θ).
  • Cotangent - reciprocal of tangent (cot θ = 1 / tan θ).
  • Vector - a directed line segment.  The length of the segment indicates magnitude or amount in a measurement and the direction of the segment, indicated with an arrow, indicates the direction of the measurement
Basic Rules of Angles
  • Vertical angles are always congruent!
  • The alternate interior angles of parallel lines cut by a transversal are congruent. 
  • The alternate exterior angles of parallel lines cut by a transversal are congruent

Shapes and Figures

  • Pythagorean Theorem: a2 + b2 = c2.
  • 3 : 4 : 5 right triangle: legs that are 3 and 4 units long resulting in a hypotenuse that is 5 units long.
  • 5:12:13 right triangle: legs that are 5 and 12 units long resulting in a hypotenuse that is 13 units long.
  • 30-60-90: when the angles are 30, 60 and 90 degrees, the sides are in ratios of 1 : √3 : 2 .
  • 45-45-90: when the angles are 45, 45 and 90 degrees, the sides are in ratios of
    √2 : √2 : 2 .
  • All regular polygons: if “n” is the number of sides, then the sum of the interior angles may be found by using: ( n – 2 ) ( 180˚ )

Area and Volume Formulas

  • It is possible to approximate the area of a figure by using smaller figures, such as triangles and rectangles, to approximate the figure.

  • We can break the figure into a number of rectangles and find the area of each:
    3x2 + 3x4 + 3x6.5 + 3x11 = 70.5 square units

  • This may be done alternatively:
    3x2 + 3x4 + 3x6.5 = 37.5 square units
  • We can average this and the previous result to get a better approximation than either alone: 59 square unit
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