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### Transcript of KEYSTONE RefEFERENCE - Intercept Formula: y = mx + b Standard Equation of a Line: Ax + By = C y 1 +...

• Properties of Circles

x

nTangent-Chord

x = n12

a

cx

d

b

m n

2 Chords

a b = c d

x = (m + n)12

a

c

xb

mn

Tangent-Secant

a2 = b (b + c)

x = (m n)12

a

x

b

m n

2 Tangents

a = b

x = (m n)12

Inscribed Angle

x = n12x

n

2 Secants

b (a + b) = d (c + d )

x = (m n)12

a

cx

d

bm 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

hypotenuse

opposite

hypotenusesin =

hypotenusecos =

opposite

Pythagorean Theorem:

a 2 + b 2 = c 2

If a right triangle has legs withmeasures a and b and hypotenusewith measure c, then...

Coordinate Geometry Properties

Distance Formula: d = (x2 x 1)2 + (y2 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 22

x 1 + x 22

y 2 y 1x 2 x 1

Formulas that you may need to solve questions on this exam are found below.

You may use calculator or the number 3.14.

RefEFERENCEKEYSTONE

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 dP = b + c + d

A = bh12

Sum of angle measures = 180(n 2), where n = number of sides

rC = 2r A = r 2

wP = 2l + 2wA = lw

l

s

s P = 4sA = s s

b

ha P = 2a + 2bA = bh

a

h

b

A = h (a + b)12

P = a + b + c + dc d

Solid Figure Formulas

Eulers Formula for Polyhedra:

V E + F = 2

vertices minus edges plus faces = 2

r

h SA = 2r 2 + 2rhV = r 2h

SA = 2lw + 2lh + 2whV = lwh

w

h

l

r

SA = 4r 2

V = r 343

h

r

SA = r 2 + r r 2 + h 2

V = r 2h13

SA = (Area of the base) + (number of sides)(b)( )

V = (Area of the base)(h)13

12h

base

b

b

Formulas that you may need to solve questions on this exam are found below.

You may use calculator or the number 3.14.

RefEFERENCEKEYSTONE

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