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IB tutor,SAT Tutor,GRE Tutor,GMAT Tutor,MCAT Tutor,DAT Tutor,Chemistry Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,AP Chemistry Tutor,IB Chemistry Tutor,Math Tutor,SAT Math

May 30, 2018

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  • 8/9/2019 IB tutor,SAT Tutor,GRE Tutor,GMAT Tutor,MCAT Tutor,DAT Tutor,Chemistry Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,AP Chemistry Tutor,IB Chemistry Tutor,Math Tutor,S

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    Volumes & Surfaces Areas

    Shape Volume Surface Area

    Sphere V=4r / 3

    RectangularPrism

    SA = 2(lw) + (2l + 2w)h

    Cylinder

    3

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    Shape Volume Surface Area

    PyramidSA = B + n(1/2sl)

    Cube SA = 2(s ) +(4s)s = 6s

    Cone

    2

    2

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    Shape Area

    Any RegularPolygon

    Prism V = Bh

    Trapezoid h/2 (b1 + b2)

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    Surface Area of Any Prism

    (b is the shape of the ends)

    Surface Area = Lateral area + Area of twoends

    (Lateral area) = (perimeter of shape b) * L

    Surface Area = (perimeter of shape b) *L+ 2*(Area of shape b)

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  • 8/9/2019 IB tutor,SAT Tutor,GRE Tutor,GMAT Tutor,MCAT Tutor,DAT Tutor,Chemistry Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,AP Chemistry Tutor,IB Chemistry Tutor,Math Tutor,S

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  • 8/9/2019 IB tutor,SAT Tutor,GRE Tutor,GMAT Tutor,MCAT Tutor,DAT Tutor,Chemistry Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,AP Chemistry Tutor,IB Chemistry Tutor,Math Tutor,S

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  • 8/9/2019 IB tutor,SAT Tutor,GRE Tutor,GMAT Tutor,MCAT Tutor,DAT Tutor,Chemistry Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,AP Chemistry Tutor,IB Chemistry Tutor,Math Tutor,S

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    RHS Congruence

    - !RHS Right Angle Hypotenuse Side When the right angle and the

    hypotenuse and the given side are

    equal for a right angle trianglethen we say that the given 2.triangles are congruent

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    Example proving RHS congruence

    E

    DA

    FCB

    < =< =B E 90 degrees = ( )AC DF hypotenuse = ( )BC EF given side

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    Example proving AAA congruence

    A

    B

    P

    O

    Q

    In this figure QA andPB are perpendiculars

    .to AB If AO is equal to

    , , &10cm BO equal to 6cm,PB equal to 9cm Find

    .AQ

    Let us consider the

    triangles OAQ and OBPcongruent.

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    In a parallelogram if one angle A is equal to

    110 degrees find the remaining angles?

    All sides of a parallelogram have to equal.360 degrees So if Angle A is 110 degrees

    then = + + +360 110 B C D- =-110 110 = + +250 B C D =D also s 110

    - =360 220 140 & = .So B C 70

  • 8/9/2019 IB tutor,SAT Tutor,GRE Tutor,GMAT Tutor,MCAT Tutor,DAT Tutor,Chemistry Tutor,Calculus Tutor,Precalculus Tutor,Algebra Tutor,AP Chemistry Tutor,IB Chemistry Tutor,Math Tutor,S

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    If the diagonals of a parallelogram are

    ,equal then show it is a rectangle? .h e o r em 1 1 1 I f AB C D i s a p ar al le l o g r a m

    h e n i ts no nc on se c u t i v e s i d e s a nd i ts.o n c o n se c ut iv e an g l e s a r e eq ua l

    = , =ro o f W e n ee d to p r o v e t h a t A B C D B C.D

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    SASSide/Angle/Side

    SAS- If 2 sides and the included angleare congruent to 2 sides and the

    included angle of a 2nd

    triangle, the 2triangles are congruent. And includedangle is an angle created by 2 sides of

    a triangle.

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    SSSSide/Side/Side

    It is a rule that is used in geometry toprove triangles congruent. The rule

    states that if 3 sides on 1 triangle arecongruent to 3 sides of a 2nd triangle,the 2 triangles are congruent.

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    AAAAngle/Angle/Angle

    If in 2 triangles, corresponding anglesare equal, then their corresponding

    sides are in the same ratio and hencethe 2 triangles are similar.

    b

    a

    fc

    d

    e

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    ASAAngle/Side/Angle

    ASA is a rule used in geometry to provetriangles are congruent. The rule

    states that if 2 angles and theincluded side of one triangle arecongruent to 2 angles and the included

    side of another triangle, the trianglesare congruent.

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    AASAngle/Angle/Side

    AAS is used in geometry to provetriangles are congruent. The rules

    state that if 2 angles and a non-included side of 1 triangle arecongruent to 2 angles and the

    corresponding non-included side ofanother triangle the 2 triangles arecongruent.

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    Corresponding Parts of Congruent

    Triangle Are Congruent/Equal When 2 triangles are congruent, all 6pairs of corresponding parts {angles &

    sides} are congruent. This statementis usually simplified as correspondingparts of congruent triangles are

    congruent.

    If

    then the following conditions are true:

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    E q u i v a l e n c er e l a t i o n s

    Reflexivity: a~ a*Every triangle is congruent to itself

    Symmetry: if a~ b then b~ a

    Transitive: if a~ band b~ cthen a~ c.

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    123 4

    5678

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    Supplementary Angles

    A pair of angles are supplementary iftheir respective measures sum to

    180. If the two supplementary angles are

    adjacent (i.e. have a common vertex

    and share a side, but do not have anyinterior points in common) their non-shared sides form a line.

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    Complementary Angles

    A pair of angles are complementary ifthe sum of their angles is 90.

    If the two complementary angles areadjacent (i.e. have a common vertexand share a side, but do not have any

    interior points in common) their non-shared sides form a right angle.

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    Area of Circle= r

    Arc length= circumference-2r* Area/360

    Arc length=Circumferencemultiplied by r divided by 2r

    Area of a sector= A= mAB/360

    * r

    (

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    What =

    http://en.wikipedia.org/wiki/Image:Pi-unrolled-720.gif
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    SHAPE AREA PERIMETER

    Square 2 4s

    Rectangle lw +2l 2w

    Triangle /bh 2 Add all thesides

    Trapezoid( + ) /a b h 2 Ad