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Honors Geometry – EOC Review Study Guide
Chapter 1 – Tools of Geometry
A
C
Chapter 2 – Logic and Reasoning
Conditional: an if-then statement
Hypothesis: the if part of a conditional (p)
Conclusion: the then part of a conditional (q)
B
AB  line AB
AB  segment AB
Conditional: p  q
Converse: q  p (swap hypothesis and conclusion)
Inverse: ~ p ~ q (negate hypothesis and conclusion)
Contrapositive: ~ q ~ p (negate and swap both)
AB  ray AB
AB  length of segment AB
Segment Addition Postulate: AC + CB = AB
A conditional and its contrapositive are logical equivalents.
1
3
4
Biconditional: a conditional and its converse are both true
and combined into one statement with “if and only if”
2
5
Definitions are biconditionals
Adjacent angles: 3 and 4
Vertical angles: 2 and 3 (  )
Linear pair: 1 and 3 (sum = 180
Counterexample: a specific example where the hypothesis of
a conditional is true but the conclusion is false.
Collinear: on the same line
Coplanar: in the same plane
Skew lines: Non-coplanar lines and never intersect
Law of detachment:
If it is raining, then I wear a raincoat. It is raining.
Conclusion: I wear a raincoat
 x2  x1    y2  y1 
2
Distance formula:
If it is Friday, then I am happy. I am happy.
Conclusion: none
2
 x1  x2 y1  y2 
,

2 
 2
Midpoint formula: 
Undefined terms: point, line, and plane
Postulate (or Axiom): accepted as true, not proven
Theorem: something that is proven
Law of Syllogism:
If it is raining, then I wear a raincoat
If I wear a raincoat, then I will look silly
Conclusion: If it is raining, I will look silly
Chapter 3 – Parallel Lines
If lines are parallel then
Alternate Interior: 3,6
Alternate Exterior: 1,8
Corresponding: 2,6
Same-side Interior: 3,4
Same-side Exterior: 1,7
1
3
5
7
2
4
6
8
Parallel lines have the same slope.
Perpendicular lines have opposite, reciprocal slopes.
1
2
Alternate Interior: 
Alternate Exterior: 
6
5
Corresponding:

7 8
Same-side Interior: = 180
Same-side Exterior: = 180
Use converses to prove lines are parallel.
3
4
Sum of interior angles in a polygon is  n  2 180 .
Measure of a interior angle of a regular polygon is  n  2 180
n
Classification vocabulary
Polygon
Regular polygon
Concave
Convex
Triangle, equilateral, pentagon, hexagon, heptagon,
octagon, nonagon, decagon and dodecagon
Sum of the measures of exterior angles is 360.
Measure of a single exterior angle is 360
n
Chapter 4 – Congruent Triangles
Scalene Triangle: no sides 
Isosceles Triangle: at least two sides 
Equilateral Triangle: all three sides 
Chapter 5 – Relationships in Triangles
Special segments of a triangle:
Median – goes thru vertex and midpoint or opposite side
Intersection is called the Centroid.
Acute Triangle: all angles less than 90
Obtuse Triangle: one angle greater than 90
Right Triangle: one right angle
Altitude – goes thru vertex and is  to opposite side
Intersection is called the Orthocenter
Isosceles Theorem: if 2 sides are  then the opposite
angles are  .
Converse: if 2 angles are  then sides opposite are 
Angle Bisector – bisects a vertex angle
Intersection is called the Incenter
Angle Sum Theorem: sum of angles in a triangle is 180
Exterior Angle Theorem: Exterior angle = sum of 2
remote interior angles.
3rd Angle Theorem: If 2 angles of two triangles are
 then the 3rd angles are also 
Ways to prove triangles are
SSS
SAS
ASA
AAS
HL

Midsegment – connects two midpoints of two sides
Midsegment is parallel to 3rd side and ½ its length
Longest side of a triangle is opposite the largest angle.
Smallest side of a triangle is opposite the smallest angle.
:
Use CPCTC after proving triangles are
Perpendicular Bisector – goes thru midpoint and is
Intersection is called the Circumcenter
Triangle Inequality Theorem: The sum of any two sides of a
triangle is greater than the length of the 3rd side.

The measure of the 3rd side of a triangle must be less than
the sum of the other two sides and greater than their
difference. (If two sides and 3 and 7 then the 3 rd side must
be 4  x  10
Chapter 6 - Quadrilaterals
To classify a parallelogram:
Are both pairs of opposite sides //?
Are all sides  ?
Are all four vertices right angles?
Are the diagonals  ?
Trapezoid:
median 
1
 b1  b2 
2
Kite:
2 pairs of adjacent,  sides
But opp. Sides R NOT 
Chapter 7 & 9 – Right Triangles
Chapter 8 - Similarity
Cross Products
Ways to prove triangles are ~:
AA ~
SAS ~
SSS ~
a c
=
b d
ad = bc
Pythagorean Theorem: c2 = a2 + b2
Right triangle if c2 = a2 + b2
Obtuse triangle if c2 > a2 + b2
Acute triangle if c2 < a2 + b2
Proportions in Triangles
45-45-90 triangle:
a c
=
b d
30-60-90 triangle:
x 2
a e
=
h f
x 3
m
p
n
m p
=
n q
q
m+n p+q
=
n
q
Trigonometry
sin() =
a c
=
x a
opp
hyp
cos() =
adj
hyp
tan() =
opp
adj
To find the angle, you must do the inverse!
Geometric Mean (Football—Mean Joe Green)
h x
=
y h
Soh Cah Toa
sin 1 cos1 tan 1
b c
=
y b
\
Angle of Elevation (E)
D
Angle of Depression (D)
E
Chapter 11 – Circles
Vertex of angle is INSIDE the circle.
Central Angle: vertex of the angle
is at the center of the circle.
A
C
mACB = m AB
m1 =
B
m2 =
Inscribed Angle: vertex of the angle
C
is ON the circle.
mACB =
1
2
m2 =
1
2
1
2
B
m1 =
A
C
1
2
D
1
B
1
2
A
C
D
( mCB  mAD )
BD bisects
1
B
BD bisects AC
1 2
B
2
( mCB  mAD )
Properties of Radius BD
m1 = 90
m ACB
m AB
2
C
( mCD  mAB )
Vertex of the angle is
OUTSIDE the circle.
m AB
Tangent and chord intersect
on the circle.
m1 =
A
1
AC
A
A
D
1
B
C
b
a d
c
c
a
b
a·b=c·d
c
a·b=c·d
b
d
a
a2 = b · c
Chapter 7 - Area
Circle
Area = πr2
Chapter 7 - Area
r = radius
d = diameter
Triangle
Area =
Circumference = 2πr
OR
Circumference = πd
Length of an Arc AB
L=
m
360
b = base
1
bh
2
h = height
Square
Area = s2
s = side
Rectangle
Area = bh
b = base
h = height
Parallelogram
Area = bh
b = base
h = height
• 2πr
Area of a Sector
Area =
m
360
•
m = measure of
central angle
r = radius
πr2
Rhombus
Area =
Area of a Segment
Area =
m
360
•
πr2 - ½bh
m = measure of
central 
r = radius
b = base of triangle
h = height of
triangle
Area =
2
ap
1
d 1d 2
2
d2 = diagonal 2
Kite
Area =
d1 = diagonal 1
1
d 1d 2
2
d2 = diagonal 2
Trapezoid
Regular Polygon
1
d1 = diagonal 1
Area =
a = apothem
p = perimeter
r = radius
1
b1 = base 1
h(b1 + b2)
2
b2 = base 2
Equilateral Triangle
Area =
Always pull out a small triangle to find a and p
s
2
4
3
s = side
Chapter 10 – Volume
Prisms
L = ph
T = L + 2B
Pyramids
L = ½ pl
T=L+B
V = Bh
V = Bh
1
3
p = perimeter of base
B = area of base
h = height
l = slant height
Cylinders
L = 2πrh
T = 2πr(h+r)
Cones
L = πrl
T = πr l(h+r)
V = πr2h
V=
1
3
r = radius
h = height
l = slant height
πr2h
Spheres
Euler’s Formula
V–E+F=2
T = 4πr2
V=
4
πr3
3
V = vertices
E = edges
F = faces