KEYSTONE                                                                          R efEFERENCE 
                                                         GEOMETRY FORMULA SHEET ─ PAGE 1 
                                                       Formulas that you may need to solve questions on this exam are found below. 
                                                                          You may use calculator π or the number 3.14. 
                                            Properties of Circles                                                              Right Triangle Formulas 
                   Angle measure is represented by x. Arc measure is represented                                                        Pythagorean Theorem: 
                   by m and n. Lengths are given by a, b, c, and d. 
                                                                                                                           c                 If a right triangle has legs with 
                                                                                                           a                                 measures a and b and hypotenuse 
                                                                       Inscribed Angle                                                       with measure c, then... 
                                                n°                                                                      b                      2       2       2 
                                x°                                                1                                                          a    +  b   =  c 
                                                                             x =     n 
                                                                                  2 
                                                                                                                                        Trigonometric Ratios: 
                                                                                                                                                         sin  =      opposite 
                                         x°                             Tangent-Chord                                                                               hypotenuse 
                                                n°                                1 
                                                                             x =     n                                         hypotenuse                             adjacent 
                                                                                  2                    opposite                                          cos  = 
                                                                                                                                                                    hypotenuse
                                                                                                                                     
                                                                                                                         adjacent                                    opposite 
                                                                            2 Chords                                                                     tan  =     adjacent
                           a            d 
                     m°        x°               n°                         a · b = c · d 
                           c            b                                      1 
                                                                         x =      (m + n)
                                                                               2 
                                                                                                                          Coordinate Geometry Properties 
                                                    a 
                                                     x°                Tangent-Secant                                                                        2              2 
                                                                                                                Distance Formula:      d =      (x  – x  )  +  (y  – y  )  
                                          n°            b                  2                                                                         2     1        2     1
                                                                             
                                                                         a = b (b + c) 
                     m°                                                                                                           x   + x      y   + y 
                                                                              1                                                    1      2      1     2 
                                                                         x =      (m − n)                       Midpoint:            2      ,      2 
                                         c                                    2 
                                                                                                                                  y   − y 
                                                                                                                Slope:      m  =    2     1 
                                                                                                                                  x   − x 
                                                                                                                                    2     1 
                                     a                                     2 Secants 
                                                                                                                Point-Slope Formula:      (y   − y  )  = m(x   − x  ) 
                                                        b             b (a + b)  = d (c + d  )                                                        1               1
                     m°                         n°  x° 
                                    c                   d                      1                                Slope Intercept Formula:      y = mx + b 
                                                                         x =      (m − n)
                                                                               2 
                                                                                                                Standard Equation of a Line:            Ax + By = C 
                                                     a                    2 Tangents 
                     m°                         n°         x°                 a = b 
                                                                               1 
                                                     b                   x =      (m − n)
                                                                               2 
                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. 
                                                                                              KEYSTONE                                                                                                                                                              R efEFERENCE 
                                                                                                                       GEOMETRY FORMULA SHEET ─ PAGE 2 
                                                                                                              Formulas that you may need to solve questions on this exam are found below. 
                                                                                                                                                    You may use calculator π or the number 3.14. 
                                                                                         Plane Figure Formulas                                                                                                                                            Solid Figure Formulas 
                                                                                                                                   P =  4s                                                                                                                                             h                                                         
                                                                                                            s                                                                                                                                                                                            SA = 2lw + 2lh + 2wh 
                                                                                                                                   A = s  ·  s                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                         V = lwh 
                                                                                        s                                                                                                                                                                                        w 
                                                                                                                                                                                                                                           l 
                                                      w                                                                            P =  2l  +  2w                                                                                                                                                              2 
                                                                                                                                   A = lw                                                                                                                                              SA =  4 r  
                                                                                                                                                                                                                                                         r                                         4         3 
                                                                                                                                                                                                                                                                                                      
                                                                                         l                                                                                                                                                                                             V = 3  r 
                                                                                                                                                          
                                                         a                                    h                                    P = 2a + 2b
                                                                                                                                   A = bh                                                                                                                                                                      2 
                                                                                                                                                                                                                                                                                       SA = 2  r   + 2 rh
                                                                                                                                                                                                                                                                       h                              
                                                                                  b                                                                                                                                                                                                                     2
                                                                                                                                                                                                                                                                                       V  =  r   h 
                                                                                            a                                                                                                                                                          r 
                                                             c                                                        d                      P = a + b + c + d 
                                                                                                 h                                                     1                  
                                                                                                                                             A =  h (a + b)
                                                                                                                                                       2                                                                                                                                                      2                       2           2 
                                                                                            b                                                                                                                                                 h                                         SA = r    +  r                           r     +  h 
                                                                                                                                                                                                                                                                                                   1          2
                                                                                                                                                                                                                                                                                        V =     r   h
                                                                                                                                                                                                                                                             r                                     3 
                                                                     c                                       d                     P = b + c + d 
                                                                                         h                                                   1
                                                                                                                                             
                                                                                                                                   A = 2bh 
                                                                                                                                                                                                                                                                                             SA = (Area of the base) + 
                                                                                                                                                                                                                                                                                                                                                       
                                                                              b                                                                                                                                                                                                                     1 
                                                                                                                                                                                                                                                                                                        (number of sides)(b)( ) 
                                                                                                                                                                                                                                                  h                                                 
                                                                                                                                                                                                                                                                                                    2 
                                                                                                                                                                                                                                                                       b                     V =  1(Area of the base)(h)
                                                                                                                                                                                                                                      base                                                                  
                                                                                                                                                                                                                                                                                                          3 
                                                                                                                                                 
                                                                                                 r                                    C = 2  r                                                                                            b 
                                                                                                                                                       2 
                                                                                                                                      A  =  r  
                                                                                                                                                                                                                                            Euler’s Formula for Polyhedra: 
                                                                                                                                                                                                                                            V − E + F = 2 
                                                                                                                                                                                                                                                                          
                                                               Sum of angle measures = 180(n – 2), 
                                                                                                                                                                                                                                            vertices minus edges plus faces = 2 
                                                               where n = number of sides 
                                   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.