Download You have:

Chapter 7: Right Triangles and Trigonometry
You have:
2 sides of a right
triangle
You need:
Examples:
Use:
Pythagorean Theorem: a  b  c
*Remember c is always the hypotenuse (longest side)
Converse of Pythagorean Theorem:
*Be sure to check to see if a triangle exists FIRST!!*
2
the last side
3 sides of a triangle
To determine
if right, acute
or obtuse
a 45˚-45˚-90˚ triangle
and one side
another side
2
2
Right Triangle: c 2  a 2  b 2 Acute Triangle: c 2  a 2  b 2 Obtuse Triangle: c 2  a 2  b 2
hypotenuse=leg  2
Figure out if you need a leg or a hypotenuse and plug it in!
*Remember if you have a leg, and you are looking for a leg - they are equal in an isosceles triangle!
hypotenuse= 2(short leg)
long leg= short leg  3
a 30˚-60˚-90˚ triangle
and one side
the last two
sides
one angle and one
side and it is NOT a
special right triangle
another side
Trig Ratios (SOH CAH TOA)
Label your parts of the triangle with your Opposite, Adjacent, Hypo. Figure out which trig
ratio you are using and set up your equation.
2 sides
an angle
Inverse Trig Ratios
Look at what angle you want to find and label your sides with your Opposite, Adjacent,
Hypo accordingly. Set up your trig ratio then multiply each side by its inverse.
Figure out which side is which by looking at the angles (remember short leg is across from the 30˚
angle, long leg is across from the 60˚). Once you know which one you are starting with, pick an
appropriate equation to plug it into.
Rectangle
Chapter 8: Quadrilaterals
All angles are right angles
Diagonals are congruent
Parallelograms
Quadrilaterals
4 sides
Interior angles add up to 360˚
Exterior angles add up to 360˚
2 pairs of parallel lines
Opposite sides congruent and parallel
Opposite angles congruent
Diagonals bisect each other
Consecutive angles are supplementary
1 pair of parallel lines
Trapezoid
Rhombus
4 sides are equal
Diagonals are perpendicular
Diagonals bisect the angles
Isosceles Trapezoid
2 pairs of congruent base angles
Legs are congruent
Diagonals are congruent
0 pairs of parallel lines
Kite




x, y  x, y
across y-axis: x, y    x, y 
across y=x: x, y    y, x
across y=-x x, y    y, x
90˚ x, y    y, x
180˚ x, y    x, y 
270˚ x, y    y, x
Finding Segment Lengths
Polygon Formulas:
Sum of interior  ’s: (n  2)180
ONE interior  of regular polygon :
( n  2)180
n
2 pairs consecutive congruent sides
Diagonals are perpendicular
1 pair of congruent angles
Non-congruent angles are bisected by the diagonal
Chapter 9: Properties of Transformations
translation (slide): x, y  x  h, y  k
Square
Sum of exterior  ’s: 360
ONE exterior  of regular polygon:
360
n
*n: number of sides
Chapter 10: Properties of Circles
reflection (flip): across x-axis:
rotation (turn):
Tangent segments
from the same point
are congruent:
AB  CB
Secant segments
Secant and Tangent
BC  AC  DC  EC AB 2  CB  DB
ow=ow
Chords
AE  EB  DE  EC
Finding Angle Measures
glide reflection: translate, then reflect
tessellation- figures that cover a plane with no
gaps or overlap {square, triangle, hexagon}
Symmetry:
Line:
-figure has at least
one line of reflection;
folds exactly in half,
one half on top of the
other
mRPS  mRS
Point(Rotational):
can rotate the figure
180° and it looks the
same, matches onto
itself
Angle ON circle
Angle IN circle
Finding arc length
Set up a proportion:
measure of arc = length of arc
360˚
circumference
Angle OUSTIDE circle Angle at CENTER
Finding area of a sector
Set up a proportion:
measure of arc= area of the sector
360˚
area of the circle
Chapter 11 – 12: Measuring Length and Area ~ Surface Area and Volume – FORMULA SHEET
2
3
*Know Lateral Area (NO bases – just faces) vs.
Scale Factor: a ~ Ratio of Areas: a ~ Ratio of Volumes: a
2
3
Surface Area (faces & bases) vs. Volume (FILL)
b
b
b
Chapter 1: Essentials of Geometry
distance formula: d 
Chapter 2: Logic
( x 2  x1 ) 2  ( y 2  y1 ) 2
conditional: If p, then q.
pq
(Original)
qp
(Flip)
If the car is running, then the key is in the ignition.
 ( x  x 2 ) ( y1  y 2 ) 
M  1
,

2
2


 y  y1 
slope formula: m   2
 x  x 
1 
 2
converse: If q, then p.
collinear: on the same line
bisect: cut in half
complementary: add up to 90˚
supplementary: add up to 180˚
If Jenelle gets a job, then she can afford a car. If Jenelle can afford a car, then she will drive to
school. CAN CONCLUDE: If Jenelle gets a job, she will drive to school.
midpoint formula:
If the key is in the ignition, then the car is running.
inverse: If not p, then not q.
~p~q (Negate)
If the car is not running, then the key is not in the car.
contrapositive: If not q, then not p.
~q~p (Flip & Negate)
If the key is not in the car, then the car is not running.
Law of Syllogism: If a, then b. If b, then c. If a, then c.
Law of Detachment: If the hypothesis is true, then the conclusion is true.
If the measure of an angle is greater than 90˚ the angle is obtuse. The m<A is 120˚. CAN
CONCLUDE: <A is obtuse.
Chapter 3: Parallel and Perpendicular Lines
<1 & <4 are vertical angles 
<1 & <5 are corresponding angles 
<1 & < 8 are alternate exterior angles 
<3 &<6 are alternate interior angles 
<3 & < 5 are consecutive interior angles =180
Chapter 4: Congruent Triangles
Triangle Interior Angle Sum: 180°
Exterior Angle Theorem: m<1=m<2+m<3
Proving Triangles Congruent:
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
Angle-Angle-Side
parallel lines: lines that do not intersect and are coplanar
(same slopes)
perpendicular lines: lines that form a 90˚ angle
(slopes are opposite reciprocals)
skew lines: lines that do not intersect and are not in the
same plane
Chapter 5: Relationships Within Triangles
Hypotenuse-Leg
midsegment- segment parallel
to its opposite side and half the
length of its opposite side.
DE ll AC and DE 
*** Remember! No swearing or calling AAA

Chapter 6: Similar Triangles
1
AC similar: two triangles that have the same angle measures and all corresponding
2
sides have the same ratio (scale factor)
perpendicular bisector- a segment, ray, line, or plane
that is perpendicular to a segment at its midpoint.
Proving Triangles Similar:
Perpendicular Bisector Theorem- If a point is ON the
Angle-Angle Similarity Side-Side-Side Similarity
perpendicular bisector of a segment, then it is equidistant
from the endpoints of the segment.
If CP is the  bisector of AB , then
CA=CB.
angle bisector- a segment, ray, line, or plane that cuts an
angle in half.
Angle Bisector Theorem- If a point is on the bisector of an
angle, then it is equidistant from the two sides of the angle.
Ratios of ALL of the
corresponding sides
are equal
Side-Angle-Side Similarity
Ratios of the corresponding
sides are equal, and the
included angles are 
REMEMBER! If two triangles are similar and drawn on top of each other,
REDRAW them separately!!! Then set up the proportion.
AD bisects <BAC and DB  AB
and DC  AC , then DB=DC.
If
To form a triangle, the sum of two sides must be
greater than the third side.
The longest side is opposite the
largest angle; smallest angle
is opposite the shortest side.
If two sides are congruent, the triangle with the
biggest angle between the sides has the bigger third
side.
 Don’t forget to get at least 8 hours
of sleep the night before the SOL!
 Also eat a healthy light breakfast
so you aren’t focused on your
rumbling tummy!