Math-Book-GMAT-Club

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Quadrilateral A polygon with four 'sides' or edges and four vertices or corners.Types of quadrilateral:Square All sides equal, all angles 90°. See Definition of a square.Rectangle Opposite sides equal, all angles 90°. See Definition of a rectangle.Parallelogram Opposite sides parallel. See Definition of a parallelogram.Trapezoid Two sides parallel. See Definition of a trapezoid.Rhombus Opposite sides parallel and equal. See Definition of a rhombus.Parallelogram A quadrilateral with two pairs of parallel sides.Properties and Tips• Opposite sides of a parallelogram are equal in length.• Opposite angles of a parallelogram are equal in measure.• Opposite sides of a parallelogram will never intersect.‐ 67 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
• The diagonals of a parallelogram bisect each other.• Consecutive angles are supplementary, add to 180°.• The area, , of a parallelogram is , where is the base of the parallelogram and is its height.• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.A parallelogram is a quadrilateral with opposite sides parallel and congruent. It is the "parent" of some otherquadrilaterals, which are obtained by adding restrictions of various kinds:• A rectangle is a parallelogram but with all angles fixed at 90°• A rhombus is a parallelogram but with all sides equal in length• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°Rectangle A 4‐sided polygon where all interior angles are 90°Properties and Tips• Opposite sides are parallel and congruent• The diagonals bisect each other• The diagonals are congruent• A square is a special case of a rectangle where all four sides are the same length.• It is also a special case of a parallelogram but with extra limitation that the angles are fixed at 90°.• The two diagonals are congruent (same length).• Each diagonal bisects the other. In other words, the point where the diagonals intersect (cross), divideseach diagonal into two equal parts.• Each diagonal divides the rectangle into two congruent right triangles. Because the triangles are congruent,they have the same area, and each triangle has half the area of the rectangle.• where: is the width of the rectangle, h is the height of the rectangle.• The area of a rectangle is given by the formula .A rectangle can be thought about in other ways:• A square is a special case of a rectangle where all four sides are the same length. Adjust the rectangle above tocreate a square.• It is also a special case of a parallelogram but with extra limitation that the angles are fixed at 90°.‐ 68 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
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For the latest version of the GMAT
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Number TheoryDefinitionNumber Theor
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• 1 (and ‐1) are divisors of ev
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other digits: 21‐(9+8+6+9)=‐11,
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Sum of n first positive integers:Su
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Converting Decimals to Fractions•
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Operations involving the same bases
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PERCENTDefinitionA percentage is a
Page 18 and 19: Absolute ValueDefinitionThe absolut
Page 20 and 21: satisfied (‐15 is not within (‐
Page 22 and 23: FactorialsDefinitionThe factorial o
Page 24 and 25: AlgebraScopeManipulation of various
Page 26 and 27: There is a common misconception tha
Page 28 and 29: RemaindersDefinitionIf and are posi
Page 30 and 31: A. 2B. 4C. 8D. 20E. 45divided by yi
Page 32 and 33: Example #10 (hard)When positive int
Page 34 and 35: Word Problems OverviewThe Following
Page 36 and 37: Key words: less than (implies subtr
Page 38 and 39: Distance/Speed/Time Word ProblemsWh
Page 40 and 41: In the next section we will learn h
Page 42 and 43: Time(3) = Time(1) + Time(2) ‐‐
Page 44 and 45: 3*x = 5*(x ‐ 20) ‐‐> x = 50 m
Page 46 and 47: Work Word ProblemsWhat is a ‘Work
Page 48 and 49: Example 3:Working together, printer
Page 50 and 51: Advanced Overlapping Sets ProblemsS
Page 52 and 53: the writing club. If 6 students sig
Page 54 and 55: two of the courses and 1 employee h
Page 56 and 57: Consider this problem to be an over
Page 58 and 59: Median The median of a triangle is
Page 60 and 61: • The midsegment is always parall
Page 62 and 63: Equilateral triangle all sides have
Page 64 and 65: • A right triangle where the angl
Page 66 and 67: Then the triangles ABC, CHB and CHA
Page 70 and 71: Squares A 4‐sided regular polygon
Page 72 and 73: • Area ‐ The usual way to calcu
Page 74 and 75: • A circle is the shape with the
Page 76 and 77: ChordA line that links two points o
Page 78 and 79: angle.• An inscribed angle is exa
Page 80 and 81: chords.‐ This becomes the theorem
Page 82 and 83: Coordinate GeometryDefinitionCoordi
Page 84 and 85: As you can see, the distance formul
Page 86 and 87: Lines in Coordinate GeometryIn Eucl
Page 88 and 89: The equation of a straight line tha
Page 90 and 91: Positive slopeHere, y increases as
Page 92 and 93: A horizontal line has a slope of ze
Page 94 and 95: Solution: We first find the slope o
Page 96 and 97: To answer, we must find the slope o
Page 98 and 99: Example #2Q: Find the point of inte
Page 100 and 101: ParabolaA parabola is the graph ass
Page 102 and 103: Standard DeviationDefinitionStandar
Page 104 and 105: Standard deviation of is . Decrease
Page 106 and 107: ProbabilityDefinitionA number expre
Page 108 and 109: Therefore, the probability of getti
Page 110 and 111: 2) Reversal combinatorial approach:
Page 112 and 113: Combinations & PermutationsDefiniti
Page 114 and 115: 1. The total number of arrangements
Page 116 and 117: is the first termDefining Propertie
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Solution(1) a1=8, does not tell us
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CuboidA cube is the 3‐D generaliz
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ConeA cone is a 3‐D object obtain
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Volume =Surface Area w/o base =Surf
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(2) : Sum of sides = . Not sufficie
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Math-Book-GMAT-Club

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