Properties of Circles

Properties of Circles x° n° Tangent-Chord x = n 1 2 a c x° d b m° n°

• Chords

a · b = c · d x = (m + n) 1 2 a c x° b m° n° Tangent-Secant a 2 = b (b + c) x = (m − n) 1 2 a x° b m°n°

• Tangents

a = b x = (m − n) 1 2 Inscribed Angle x = n 1 2 x° n°

• Secants

b (a + b) = d (c + d ) x = (m − n) 1 2 a c x° d b m°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 θ opposite hypotenuse sin θ = adjacent hypotenuse cos θ = opposite adjacent tan θ =

Pythagorean Theorem:

a 2

• b

2 = c 2 If a right triangle has legs with measures a and b and hypotenuse with measure c, then...Coordinate Geometry Properties

Distance Formula: d = (x

2 – x 1 ) 2

• (y

2 – 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

2 2 x 1

• x

2 2 y 2 − y 1 x 2 − x 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.RefEFERENCE

KEYSTONE

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 d P = b + c + d A = bh 1 2 Sum of angle measures = 180(n – 2), where n = number of sides r C = 2πr A = πr 2 w P = 2l + 2w A = lw l s s P = 4s A = s · s b h aP = 2a + 2b A = bh a h b A = h(a + b) 1 2 P = a + b + c + d cd Solid Figure Formulas

Euler’s Formula for Polyhedra:

V − E + F = 2

vertices minus edges plus faces = 2 r h SA = 2πr 2

• 2πrh

V = πr 2 h SA = 2lw + 2lh + 2wh V = lwh w h l r SA = 4πr 2 V = πr 34 3 h r SA = πr 2

• πr r

2

• h

2 V = πr 2 h 1 3 SA = (Area of the base) + (number of sides)(b)( ) V = (Area of the base)(h) 1 3 1 2 h base b b Formulas that you may need to solve questions on this exam are found below.You may use calculator π or the number 3.14.RefEFERENCE

KEYSTONE

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