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Name: ________________________
Date: _____________________ C o o r d i n a t e R e l a t i o n s
Unit 1 Review Sheet
Equations of a
Line:
● Standard Form
● Point-Slope Form
● Slope-Intercept
Form
Slope Formula:
Slope Formula
Line Equations
Distance Formula
Midpoint Formula
Transformation Rules
Symmetry
TOPICS COVERED: Distance Formula:
Midpoint Formula:
Symmetry Definitions:
Line Symmetry: is the imaginary line where you could fold the image
and have both halves match exactly.
Point Symmetry: it looks the same upside down!
**If a shape has an even number of lines of symmetry then the shape
will have point symmetry**
If all the sides of a shape are equal, then the number of sides is equal
to the number of lines of symmetry. (anything with the name
“regular” in front is a shape with all equal sides)
Rules for Rotation:
90⁰ clockwise
(x, y) → (y, -x)
90⁰ counterclockwise
(x, y) → (-y, x)
180⁰ (any direction)
(x, y) → (-x, -y)
Rules for Reflection
Over the x-axis: (x, y) → (x, -y)
Over the y-axis: (x, y) → (-x, y)
Over y=x: (x, y) → (y, x)
Over y= -x: (x, y) → (-y, -x)
OTHER:
Translation of (a,b)
(x, y) → (x+a, y+b)
Dilation of a
(x, y) → (ax, ay)
Name: ________________________
Date: _____________________ P a r a l l e l L i n e s c u t b y a T r a n s v e r s a l
Unit 2 Review Sheet
Types of Angles
Angle Relationships
Parallel w/ Transversal
Parallel w/ 2 Transversals
TOPICS COVERED:
TYPES OF ANGLES:
Acute– less than 90 degrees
Right– equal to 90 degrees
Obtuse– greater than 90 degrees
Straight– equal to 180 degrees
ANGLE RELATIONSHIPS:
Complementary– two or more
angles that add to 90 degrees.
Supplementary– two or more angles
that add to 180 degrees
Linear Pair– two angles that are on
the same straight line (adjacent
angles).
Vertical Angles– angles formed by
intersecting lines where the two
opposite angles are equal.
Supplementary Angles:
Exterior: ∠1 & ∠7, ∠2 & ∠8
Consecutive Interior/ Same Side Interior:
Congruent Angles
Alternate Interior: ∠3 & ∠6, ∠4 & ∠5
Alternate Exterior: ∠1 & ∠8, ∠2 & ∠7
Corresponding: ∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7,
INTERIOR
Alternate means opposite sides of
the transversal
1
3
2
8
4
5 6
7
Name: ________________________
Date: _____________________ T r i a n g l e s ( I n e q u a l i t i e s , ≅ , ~ )
Unit 3 Review Sheet
Exterior Angle Theorem
Angle/Side Relationship
Δ Inequality Theorem
Congruent Triangles
Similar Triangles
TOPICS COVERED: The exterior angle is equal to the sum of the two non-adjacent angles.
Angle/ Side Relationships
The smallest angle is opposite the small-
est side. (As well as the smallest side
being opposite the smallest angle)
The largest angle is opposite the largest
side. (As well as the largest side being
opposite the largest angle)
TRIANGLE INEQUALITY THEOREM
AB + BC > AC
AC + BC > AB
AB + AB > BC
Applying the triangle inequality theorem
Proving three segments form a triangle: Add the two smaller numbers and see if they add to be
greater than the third side.
Possible length of a missing side: (always with the larger number on top) subtract the two
numbers (left hand side) , and add the two numbers (right hand side) and put those answers into
your inequality. ____ < x < ____ Congruent Triangles
SSS, SAS, ASA, AAS
Similar Triangles
SSS-proportional, SAS, AA Properties to Remember:
Vertical Angles– are congruent & happen when two triangles meet at a point
Parallel Lines– look for alt, int. angles & corresponding angles
Bisector & Midpoint– divides lines or angles into two congruent parts
Reflexive Property– something is congruent to itself & happens when two triangles share a side or
angle
Perpendicular Lines– form right angles and all right angles are congruent
Your three letter acronym is al-
ways beside a statement that
looks like
When you are proving some-
thing other than two triangles
congruent your last reason
should be CPCTC
Read the given information for
clues & MOST OF ALL LABEL
THE PICTURE!!!!!!!!!!!
WHEN DOING A PROOF
CPCTC– Corresponding Parts of Congruent Triangles are Congruent
A
B
C X
Y
Z
ΔABC ~ ΔXYZ AB BC AC
= =
∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z
≅ “congruent to”
~ “similar to”
= “equal to”
Name: ________________________
Date: _____________________ R i g h t T r i a n g l e s
Unit 4 Review Sheet Pythagorean Theorem
Acute vs. Obtuse vs. Right
Special Right Triangles
Trigonometry
TOPICS COVERED:
Pythagorean Theorem:
a2 + b2 = c2
How to prove Triangles are Acute, Obtuse, or Right
Acute: a2 + b2 > c2
Obtuse: a2 + b2 < c2
Right: a2 + b2 = c2
**Always think in terms of c**
When to use Pythagorean Theorem Vs. Trigonometry:
Start with a Right Triangle
What are you solv-
ing for?
A Side and an Angle... Two Sides... Are you given…..
An Angle A Side
Then you use..
Trigonometry Pythagorean Theorem
The three different
Trigonometric functions are:
SOHCAHTOA
θ
H
O
A
When solving for an angle in your calculator make sure to press 2nd,
then your trig function, and then your trigonometric ratio (aka your
fraction).
Special Right Triangles
30 60 90
45 45 45
Name: ________________________
Date: _____________________ L o g i c
Unit 5 Review Sheet
Conditional Statement
Converse
Inverse
Contrapositive
Biconditional
Laws of Logic
Symbolic Representation
TOPICS COVERED:
Conditional Statement: (if-then form): If it is a right angle, then it measures 90 degrees. (p→q)
Converse: (switch order): If the angle measures 90 degrees, then it is a right angle. (q→p)
Inverse: (negate the conditional): If it is not a right angle, then it does not measure 90 degrees. (~p→~q)
Contrapositive: (converse of the inverse): If the angle does not measure 90 degrees then it is not a right angle. (~q→~p)
Biconditional: (if and only if): The angle is right if and only if it measures 90 degrees.(p↔q)
Law of Syllogism:
Option 1: Verbal
If I go grocery shopping, then I buy milk.
If I buy milk, then I’ll eat cereal.
Therefore: If I go grocery shopping, then I eat cereal
Option 2: Symbolic
p → q
q → r
∴ p → r
Law of Detachment:
Option 1: Verbal
If you are a duck, then you waddle.
Larry is a duck.
Therefore: Larry waddles
Option 2:
p→q
P
∴ q
“All” “Some” “None” “And” “Or”
All of A is in B Some of A is in B None of A is in B A and B A or B
B
A
B
A
B
A
B
A
B
A
Name: ________________________
Date: _____________________ P o l y g o n s & Q u a d r i l a t e r a l s
Unit 6 Review Sheet Classifying Polygons
Interior angles of polygons
Exterior angles of polygons
Quadrilaterals and their Properties
TOPICS COVERED:
Sum of the Interior for any polygon:
Each interior angle of a
regular polygon:
Sum of the exterior angle of
any polygon:
Classifying Polygons:
● Regular: all sides and angles are congruent.
● Equilateral: only sides are congruent.
● Equiangular: only angles are congruent.
● Irregular: no sides or angles are congruent.
-agons
3-triangle
4– quadrilateral
5– pent
6– hex
7– hept
8– oct
9– non
10– dec
Parallelogram
1. Sides
Opposite sides are parallel
Opposite sides are congruent
2. Angles
Opposite angles are congruent.
Consecutive angles are
supplementary
The sum of the interior angles
are 360.
3. Diagonals
Diagonals bisect each other.
Diagonals form congruent trian
gles.
Rectangle
Is a parallelogram.
1. Angles
All angles are congruent (90 de
grees)
2. Diagonals
Diagonals are congruent.
Thus, all four segments formed
are congruent
Rhombus
Is a parallelogram
1. Sides
All sides are congruent
2. Diagonals
Diagonals bisect angles
Diagonals are perpendicular
This means they form 90 degree
angles.
Square
Is a rectangle and a rhombus,
both of which are a parallel
gram. Which means it has all the
properties of the three.
Trapezoid
Parallelogram
Rect. Square Rhom.
Trapezoid
Isos. Trap.
Name: ________________________
Date: _____________________ C i r c l e s
Unit 7 Review Sheet
Parts of a Circle
Angle & Arc Measures
Segment Length
Arc Length & Sector Area
Equations of Circles
TOPICS COVERED:
Radius: Measures the distance from the center
to a point on the circle.
Tangent: Touches the circle at exactly one
point.
Secant: Passes through a circle at two points.
Chord: A line whose endpoints are on the
circle.
Diameter: Is a chord that goes through the
center of the circle
A) B) C) D)
Angle & Arc Measures:
● If the angle formed is
inside the circle (picture
A) then you add the two
arcs formed by the an-
gle and its vertical angle
● If the angle formed is
outside the circle
(picture B and C) you
subtract the two arcs
formed. Always put the
larger arc first when
subtracting!
Segment Length:
● If two chords intersect like
picture A, use:
(part)(part)=(part)(part)
● If two secants intersect like
in picture B, use:
(whole)(out)=(whole)(out)
If a secant and a tangent
intersect like in picture C,
use:
(whole)(out)=(whole)(itself)
Tangent = Tangent like in
Arc Length & Sector
Area
Arc Length:
Sector Area:
Equation of a Circle:
Center: (h, k)
Radius: r
Formula:
When solving for the cen-ter use the midpoint for-
mula.
When solving for the ra-dius use the distance
formula.
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