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.