Geometry – Things to Remember! 
            3-D Figures:                                Regular Solids:                             Locus Theorems:                  
                                                                                                    Fixed distance from point.      Fixed distance from a line. 
            Prism:  V = Bh                              Tetrahedron – 4 faces 
                           1                            Cube – 6 faces 
            Pyramid:  VB=      h                        Octahedron – 8 faces                                                                                
                           3                                                                                             
                              2                     2   Dodecahedron – 12 faces                     Equidistant from 2 points.      Equidistant 2 parallel lines.
            Cylinder:  Vr=π    h; SA=+22πrh      πr   Icosahedron – 20 faces 
            Cone:       1    2                  2
                   Vr= π h;  SA=+sπr πr                                                                                                                     
                        3                               Triangles: 
                          4   3             22                                                                             
            Sphere:  Vr=   π ;  SA==4πr        πd       By Sides:                                                 Equidistant from 2
                          3                             Scalene – no congruent sides                                 intersecting lines 
                                                        Isosceles – 2 congruent sides                                                              
                                                        Equilateral – 3 congruent sides 
            Polygon Interior/Exterior Angles:           By Angles:                                 Congruent Triangles 
            Sum of int. angles = 180(n−2)               Acute – all acute angles                    SSS                             NO donkey theorem 
            Each int. angle (regular) = 180(n−2)        Right – one right angle                     SAS                                   (SSA or ASS) 
                                             n          Obtuse – one obtuse angle                   ASA 
            Sum of ext. angles = 360                    Equiangular – 3 congruent angles(60º)       AAS 
                                         360            Equilateral ↔ Equiangular                   HL (right triangles only) 
            Each ext. angle (regular) =  n                                                          
                                                        Exterior angle of a triangle equals the    CPCTC (use after the triangles are congruent) 
            Related Conditionals:                       sum of the 2 non-adjacent interior         Inequalities: 
            Converse: switch if and then                angles.                                    --Sum of the lengths of any two sides of a triangle is greater 
            Inverse:  negate if and then                                                           than the length of the third side. 
            Contrapositive:  inverse of the converse    Mid-segment of a triangle is parallel      --Longest side of a triangle is opposite the largest angle. 
            (contrapositive has the same truth value    to the third side and half the length of   --Exterior angle of a triangle is greater than either of the 
            as the original statement)                  the third side.                            two non-adjacent interior angles. 
                                                                                                    
            Pythagorean Theorem:                        Similar Triangles:                         Mean Proportional in Right  Triangle: 
             222                                        AA                                         Altitude Rule:                              Leg Rule: 
            ca=+b                                       SSS for similarity 
            Converse:  If the sides of a triangle 
                     222                                SAS for similarity 
            satisfy ca=+b then the triangle is a  Corresponding sides of similar                                                                                      
            right triangle.                             triangles are in proportion.                
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                 Parallels:  If lines are parallel …                                           Quadrilaterals:                                                               Transformations: 
                                                                                                 Parallelogram:  opp                       Trapezoid:                                                                                 Glide 
                                                                                                 sides parallel                            Only one set                                                                          reflection is 
                                                                                                 opp sides =                               parallel sides.                                                                      composition 
                                                                                                 opp angles =                                                                                                                  of a reflection 
                                                                                                 consec. angles supp                       Median of trap is                                                                          and a 
                 Corresponding angles are equal.                                                 diag bis each other                       parallel to both                                                                      translation. 
                 m<1=m<5, m<2=m<6, m<3=m<7, m<4=m<8                                              Rectangle: add 4 rt                       bases and = ½                                                                        
                                                                                                                                           sum bases.                                                                             Isometry – 
                 Alternate Interior angles are equal.                                            angles, diag. =                                            : 
                 m<3=m<6, m<4=m<5                                                                Rhombus:  add 4 =                         Isosceles Trap:                                                                      keeps length. 
                 Alternate Exterior angles are equal.                                            sides, diag. perp, diag                   legs =                                                                               
                 m<1=m<8, m<2=m<7                                                                bisect angles.                            base angles =                                                                        Orientation – 
                 Same side interior angles are supp.                                             Square:  All from                         diagonals =                                                                            label order 
                 m<3+m<5=180,    m<4+m<6=180                                                     above.                                    opp angles supp                                                         
                 Circle Segments                                                               Circle Angles: 
                 In a circle, a radius perpendicular to a chord                                Central angle = arc         Inscribed angle = half arc           Angle by tangent/chord = half arc 
                 bisects the chord. 
                 Intersecting Chords Rule: 
                 (segment part)•(segment part) =                                                                                                                                                                              
                                      (segment part)•(segment part)                             
                 Secant-Secant Rule:                                                           Angle formed by 2 chords      Angle formed by 2 tangents, or 2 secants, or a tangent/secant 
                  (whole secant)•(external part) =                                             = half the sum of arcs                   = half the difference of arcs 
                              (whole secant)•(external part) 
                 Secant-Tangent Rule: 
                                                                                     2 
                  (whole secant)•(external part) = (tangent)                                                                                                                                                                         
                 Hat Rule:  Two tangents are equal. 
                 Slopes and Equations:                                                         Coordinate Geometry Formulas:                                                 Circles: 
                           vertical change                 y − y                               Distance Formula:                                                             Equation of circle center at origin: 
                                                             21
                  m=                                   =.                                                             22 222
                         horizontal change                 x −x                                 dx=−()x+(y−y)                                                                 x + yr=              where r is the radius. 
                                                             21                                             21 21                                                            Equation of circle not at origin: 
                  ym=+xb  slope-intercept                                                      Midpoint Formula: 
                                                                                                                                                                                        222
                  yy−=m(x−x) point-slope                                                                       x ++xyy                                                        ()x − hy+−(k)=r where (h,k) is the 
                          11                                                                                ⎛⎞
                                                                                                                1212
                                                                                                (,xy)=                   ,                
                                                                                                            ⎜⎟center and r is the radius. 
                                                                                                                   22
                                                                                                            ⎝⎠ 
                  
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