KEYSTONE RefEFERENCE 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 with measure c, then... n° Inscribed Angle b 2 + 2 = 2 x° 1 a b c x = n 2 Trigonometric Ratios: opposite sin θ = x° Tangent-Chord hypotenuse n° = 1 x n hypotenuse adjacent 2 opposite cos θ = hypotenuse θ adjacent opposite tan θ = 2 Chords adjacent d a · = · m°x° n° a b c d c 1 b x = (m + n) 2 Coordinate Geometry Properties a x° Tangent-Secant = – 2 + – 2 b Distance Formula: d (x2 x 1) (y2 y 1) n° 2 = + a b (b c) m° x + x y + y 1 1 2 , 1 2 x = (m − n) Midpoint: c 2 2 2 y − y = 2 1 Slope: m − x 2 x 1 a 2 Secants Point-Slope Formula: (y − y ) = m(x − x ) b + = + 1 1 b (a b) d (c d ) m° n° x° 1 c d x = (m − n) Slope Intercept Formula: y = mx + b 2 Standard Equation of a Line: Ax + By = C a 2 Tangents a = b m° n° x° 1 x = (m − n) b 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 RefEFERENCE 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 = s P 4s h SA = 2lw + 2lh + 2wh A = s · s V = lwh s w l P = 2l + 2w w = 2 A = lw SA 4 r 4 r V = r 3 l 3 P = 2a + 2b a h A = bh = 2 + h SA 2 r 2 rh b V = r 2h r a P = a + b + c + d c d h 1 A = h(a + b) 2 2 2 2 SA = r + r r + h b h 1 V = r 2h r 3 P = b + c + d c d h = 1 A 2 bh SA = (Area of the base) + b 1 (number of sides)(b)( ) h 2 b 1 V = (Area of the base)(h) base 3 = C 2 r b r A = r 2 Euler’s Formula for Polyhedra: V − E + F = 2 Sum of angle measures = 180(n – 2), where n = number of sides vertices minus edges plus faces = 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..