Keystone Reference Geometry Formula Sheet - Page 1

Sep 15, 2026

Uploaded by Callum

Geometry formula sheet providing essential reference formulas for solving exam questions. Covers properties of circles including inscribed angles, tangent-chord relationships, and secant-tangent and tangent formulas, with arc and angle measures represented by variables. Includes right-triangle relationships such as the Pythagorean theorem and trigonometric ratios, plus coordinate geometry tools including distance, midpoint, slope, point-slope, and slope-intercept forms. Includes plane and solid figure formulas on the referenced pages.

LanguageEnglish

CategoryExam

FormatPDF

Pages2

Reading Time5 min

AccessFree to download

Properties of Circles

Inscribed Angle and Arc Measure

Tangent-Chord and Tangent-Secant

Right Triangle Formulas

Pythagorean Theorem

Trigonometric Ratios

KEYSTONE REFERENCE 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 Angle measure is represented by x. Arc measure is represented by m and n. Lengths are given by a, b, c, and d. x° n° m° Inscribed Angle x = 1~~2 ~~ n Tangent-Chord x = 1~~2 ~~ n 2 Chords a · b = c · dx = 1~~2 ~~ (m + n) Tangent-Secant a 2 = b(b + c) x = 1~~2 ~~ (m − n) 2 Secants b (a + b) = d(c + d ) x = 1~~2 ~~ (m − n) 2 Tangents a = bx = 1~~2 ~~ (m − n) Right Triangle Formulas a Pythagorean Theorem: If a right triangle has legs with measures a and b and hypotenuse with measure c, then... a 2 + b2 = c2 Trigonometric Ratios: opposite sin θ = cos θ = opposite hypotenuse adjacent hypotenuse adjacent opposite tan θ = adjacent Coordinate Geometry Properties Distance Formula: d = (x2 – x1)2 + (y2 – y 1)2 Midpoint: Slope: m = x 1 + x2 2 , y 2 − y 1 x2 − x1 y 1 + y 2 2 Point-Slope Formula: (y − y 1) = m (x − x1) Slope Intercept Formula: y = mx + b Standard Equation ofa Line: Ax + By = C 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 REFERENCE 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 s P = 4s A = s · s s w P = 2l + 2 w A = lw l b P = 2a + 2b A = bh a h d b P = a + b + c + d A = ~~12~~ h (a + b) P = b + c + d A = ~~12~~bh b C = 2􀀂r A = 􀀂r2 Sum of angle measures = 180(n – 2), where n = number of sides Solid Figure Formulas h SA = 2 lw + 2 lh + 2wh V = lwh SA = 4􀀂r2 V = ~~43~~􀀂r3 h SA = 2􀀂r2 + 2􀀂 rh V = 􀀂r2 h SA = 􀀂r2 + 􀀂rr 2 + h2 V = ~~13~~ 􀀂r2 h SA = (Area of the base) + ~~12~~ (number of sides)(b)( ) V = ~~13~~ (Area of the base)(h) Euler’s Formula for Polyhedra: V − E + F = 2 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.

FAQs

What coordinate geometry formulas are listed for computing distance and line equations?

The sheet includes the distance formula, midpoint formula, slope, point-slope, slope-intercept, and the standard form Ax + By = C.

Sep 15, 2026

Uploaded by Callum