KEYSTONE RefEFERENCE - Intercept Formula: y = mx + b Standard Equation of a Line: Ax + By = C y 1 +...

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Transcript of KEYSTONE RefEFERENCE - Intercept Formula: y = mx + b Standard Equation of a Line: Ax + By = C y 1 +...

  • Properties of Circles

    x

    nTangent-Chord

    x = n12

    a

    cx

    d

    b

    m n

    2 Chords

    a b = c d

    x = (m + n)12

    a

    c

    xb

    mn

    Tangent-Secant

    a2 = b (b + c)

    x = (m n)12

    a

    x

    b

    m n

    2 Tangents

    a = b

    x = (m n)12

    Inscribed Angle

    x = n12x

    n

    2 Secants

    b (a + b) = d (c + d )

    x = (m n)12

    a

    cx

    d

    bm n

    Angle measure is represented by x. Arc measure is represented by m and n. Lengths are given by a, b, c, and d.

    Right Triangle Formulas

    a

    b

    c

    Trigonometric Ratios:

    opposite

    adjacent

    hypotenuse

    opposite

    hypotenusesin =

    adjacent

    hypotenusecos =

    opposite

    adjacenttan =

    Pythagorean Theorem:

    a 2 + b 2 = c 2

    If a right triangle has legs withmeasures a and b and hypotenusewith measure c, then...

    Coordinate Geometry Properties

    Distance Formula: d = (x2 x 1)2 + (y2 y 1)2

    Midpoint: ,

    Slope: m =

    Point-Slope Formula: (y y 1) = m (x x 1)

    Slope Intercept Formula: y = mx + b

    Standard Equation of a Line: Ax + By = C

    y 1 + y 22

    x 1 + x 22

    y 2 y 1x 2 x 1

    Formulas that you may need to solve questions on this exam are found below.

    You may use calculator or the number 3.14.

    RefEFERENCEKEYSTONE

    GEOMETRY FORMULA SHEET PAGE 1

    Copyright 2011 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.

  • Plane Figure Formulas

    c

    b

    h dP = b + c + d

    A = bh12

    Sum of angle measures = 180(n 2), where n = number of sides

    rC = 2r A = r 2

    wP = 2l + 2wA = lw

    l

    s

    s P = 4sA = s s

    b

    ha P = 2a + 2bA = bh

    a

    h

    b

    A = h (a + b)12

    P = a + b + c + dc d

    Solid Figure Formulas

    Eulers Formula for Polyhedra:

    V E + F = 2

    vertices minus edges plus faces = 2

    r

    h SA = 2r 2 + 2rhV = r 2h

    SA = 2lw + 2lh + 2whV = lwh

    w

    h

    l

    r

    SA = 4r 2

    V = r 343

    h

    r

    SA = r 2 + r r 2 + h 2

    V = r 2h13

    SA = (Area of the base) + (number of sides)(b)( )

    V = (Area of the base)(h)13

    12h

    base

    b

    b

    Formulas that you may need to solve questions on this exam are found below.

    You may use calculator or the number 3.14.

    RefEFERENCEKEYSTONE

    Copyright 2011 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.

    GEOMETRY FORMULA SHEET PAGE 2