unit 6: connecting algebra & geometry through coordinates...mar 03, 2015 · project scoring...

UNIT 6: Connecting Algebra & Geometry through Coordinates

TASK: Vocabulary

Learning Target: I can identify, define and sketch all the vocabulary for UNIT 6.

Materials Needed:

4 pieces of white computer paper.

Pencil, Pen, Markers or Color Pencils. Color is a significant aid here.

Vocabulary List (KEY CONCEPTS)

Instructions:

1. Fold the 4 pieces of white paper to create 4 flip books (teacher will direct you on folding). As

an alternative, the teacher may give you a document to fill in the definitions and sketches of

the terms.

2. On the outside cover of the Flip-Book you will write the term “VOCABULARY WORD”.

3. On the inside of the Flip-Book, there are 2 rectangles for each term. In the first rectangle

you will define the term, and in the second rectangle you will sketch a picture of what the

term would look like. Use the handout titled KEY CONCEPTS to create the Flip-Book. (You

will turn in the handout). Therefore, you will need your Flip-Book to complete this unit and for

studying purposes.

Key Terms:

These terms MUST be in your flip-book.

General geometry

Coordinate

X-intercept

Y-intercept

Slope

Endpoint

Lines

Line

Line Segment

Parallel line

Perpendicular line

Triangles

Equilateral

Isosceles

Scalene

Acute

Right Angle

Obtuse

Quadrilaterals

Square & Rhombus

Rectangle

Parallelogram

Kite

Regular Polygons

Pentagon (5 sides)

Hexagon (6)

Heptagon (7)

Octagon (8)

Calculations & Theorems

Midpoint

Distance between two

points

Pythagorean Theorem

Flip Book Unit 6: Connecting Algebra & Geometry

NAME ___________________________ DATE: _______________

Geometric Figures & Terms

Flip Book

Project Scoring

Reference Max Score

Content Complete, Thorough, Accurate 40

Neatness Use of straight edge, legible, presentable 10

Bonus: Creativeness: use of color, use of different lines,

notations, additional facts, etc. 5

Scored out of 50 55


Term Definition Diagram / Sketch

Coo

rdinate

A number used to identify the

location of a point. In a plane, there

are two coordinates that represent a

point, (x,y)

X-Int

erc

ept

Y-Int

erc

ept

Slope

End

point



Line**

A straight arrangement of pts.

There are infinitely many

points in a line. A line has no

endpoints and continues

forever in two directions.

In analytic geometry, a line in

the plane is “a set of points

whose coordinates satisfy a

given linear equation.”

Denoted by 𝑨𝑩 ⃡

Para

llel Lines*

*

Coplanar lines that do not

intersect

The slopes of parallel line are

equal to each other, but have a

different y-intercept.

Denoted by ∥

Perp

end

icular

Lines*

*

Most common: Two lines that

intersect at a right angle.

The slopes of two perpendicular

lines are negative reciprocals of

each other.

Denoted by ⊥

**From previous flip book



ALL T

riang

le

All Triangles:

A closed 3-sided figure with

three angles

The sum of the three interior

angles is always 180

Equ

ilate

ral

Iso

sceles

Sca

lene



Right

Acu

te

Obtu

se

Are

a o

f a



Qua

drilate

ral

All Quadrilaterals:

A closed 4-sided figure with

four angles. Angles can be

either convex or concave.

In Latin, “quadri” is a variant of

four, and “latus” means side

The sum of the four interior

angles is always 360

Para

llelogr

am

Rect

ang

le

Are

a o

f a R

ect

ang

le



Rhom

bus

Squ

are

Tra

pezoid

Kite


Dista

nce**

Technically it’s the amount of

space between two points

Interpretation: the shortest amount of space between two

points.

Mid

point*

*

The EXACT middle point of

a line segment.

Midpoint Postulate

(Euclidian): A line segment

has EXACTLY ONE

MIDPOINT

** From previous Flip Book


Pyth

ago

rean

Theor

em


Regular polygons.

Sides: 3

Name: Equilateral

Triangle

Each internal : 60

Sides: 4

Name: Square

Each internal : 90

Sides: 5

Name:

Each internal :

Sides: 6

Name:

Each internal :

Sides: 7

Name:

Each internal :

Sides: 8

Name:

Each internal :

Sides: 9

Name:

Each internal :

Sides: 10

Name:

Each internal :


Geometric Figures & Terms

Flip Book

KEY



Coo

rdinate

A number used to identify the

location of a point. In a plane, there

are two coordinates that represent a

point, (x,y)

X-Int

erc

ept

The point where the graph

intersects the X-Axis (when y = 0).

Usually in the form (x,0)

Y-Int

erc

ept

The point where the graph

intersects the Y-Axis (when x = 0).

Usually in the form (0,y)

The value of “b” in the slope-

intercept form of a line y = mx + b

Slope

A measure of steepness of a line.

Referred to as the “rise over the

run”

End

point

The point at each end of a line segment

or at the beginning of a ray.



Line

A straight arrangement of points.

There are infinitely many points in

a line. A line has no endpoints and

continues forever in two directions.

In analytic geometry, a line in the

plane is “a set of points whose

coordinates satisfy a given linear

equation.”

Denoted by 𝑨𝑩 ⃡

Para

llel Lines

Coplanar lines that do not intersect

Parallel Postulate (Euclidian):

through a point not on a given line,

you can constructed EXACTLY ONE

line parallel to the given line.

The slopes of parallel line are equal

to each other, but have a different

y-intercept.

Denoted by ∥

Perp

end

icular

Lines

Most common: Two lines that

intersect at a right angle.

Euclidean definition: two lines that

form congruent adjacent angles (you

need to read this definition a couple

times to get it)

The slopes of two perpendicular lines

are negative reciprocals of each

other.

Denoted by ⊥



ALL T

riang

le

All Triangles:

Three sides & three angles

The three angles always add to

180

Equ

ilate

ral

ALL THREE SIDES EQUAL

ALL 3 ANGLES ALWAYS 60

Iso

sceles

TWO SIDES EQUAL

TWO EQUAL ANGLES

Sca

lene

NO SIDES EQUAL

NO EQUAL ANGLES



Right

Has a right angle (90)

Can be isosceles or scalene

Acu

te

ALL angles less than 90

Can be equilateral, isosceles or

scalene

Obtu

se

Has an angle more than 90

Can be isosceles or scalene

Are

a o

f a

Three methods to calculate:

1. A = ½ b h

2. ½ a b sin C

3. Heron’s formula

√𝑠 ∙ (𝑠 − 𝑎) ∙ (𝑠 − 𝑏) ∙ 𝑠 − 𝑐)



Qua

drilate

ral

A polygon with four sides (edges) and

four vertices

In latin, “quadri” is a variant of four,

and “latus” means side

Angles can be either convex or concave

Sum of the interior angles always

equals 360

Para

llelogr

am

A special quadrilateral with two

sets of parallel lines.

Opposite sides are parallel AND

equal.

Opposite angles are equal;

Adjacent angles are supplementary

(add to 180)

Rect

ang

le

A special parallelogram with all

four interior angles being 90 right

angles.

Opposite sides are parallel AND

equal.

All sets of adjacent sides are

perpendicular to each other.

Are

a o

f a R

ect

ang

le



Rhom

bus

A special parallelogram with all

four sides equal to each other.

Opposite sides are parallel to

each other.

Opposite angles are equal to

each other. Adjacent angles

are supplementary (sum to

180).

Squ

are

A special rhombus with all four

sides equal to each other AND

all four interior angles being

90 right angles.

All sets of adjacent sides are

perpendicular to each other

Tra

pezoid

A special quadrilateral with one

set of parallel lines.

Kite A special quadrilateral with

two isosceles triangles with

the same base.


Dista

nce

Technically it’s the amount

of space between two

points

Interpretation: the

shortest amount of space

between two points.

Mid

point

The EXACT middle point of

a line segment.

Midpoint Postulate

(Euclidian): A line segment

has EXACTLY ONE

MIDPOINT


Pyth

ago

rean

Theor

em

In mathematics, the Pythagorean

theorem, also known as

Pythagoras's theorem, is a relation

in Euclidean geometry among the

three sides of a right triangle. It

states that the square of the

hypotenuse (the side opposite the

right angle) is equal to the sum of

the squares of the other two sides.


Regular polygons.

Sides: 3

Equilateral

triangle

Each internal angle:

60

Sides: 4

Square


90

Sides: 5

Regular pentagon


108

Sides: 6

Regular hexagon


120

Sides: 7

Regular pentagon


128.5714

Sides: 8

Regular octagon


135

Sides: 9

Regular nonagon


140

Sides: 10

Regular decagon


144

unit 6: connecting algebra & geometry through coordinates...mar 03, 2015 · project scoring...

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