unit 6: connecting algebra & geometry through coordinates...mar 03, 2015 · project scoring...
TRANSCRIPT
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
Flip Book Unit 6: Connecting Algebra & Geometry
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
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
Right
Acu
te
Obtu
se
Are
a o
f a
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
Rhom
bus
Squ
are
Tra
pezoid
Kite
Flip Book Unit 6: Connecting Algebra & Geometry
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
Term Definition Diagram / Sketch
Pyth
ago
rean
Theor
em
Flip Book Unit 6: Connecting Algebra & Geometry
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 :
Flip Book Unit 6: Connecting Algebra & Geometry
Geometric Figures & Terms
Flip Book
KEY
Flip Book Unit 6: Connecting Algebra & Geometry
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
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.
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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 ⊥
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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)
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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
Flip Book Unit 6: Connecting Algebra & Geometry
Term Definition Diagram / Sketch
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.
Flip Book Unit 6: Connecting Algebra & Geometry
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
Term Definition Diagram / Sketch
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.
Flip Book Unit 6: Connecting Algebra & Geometry
Regular polygons.
Sides: 3
Equilateral
triangle
Each internal angle:
60
Sides: 4
Square
Each internal angle:
90
Sides: 5
Regular pentagon
Each internal angle:
108
Sides: 6
Regular hexagon
Each internal angle:
120
Sides: 7
Regular pentagon
Each internal angle:
128.5714
Sides: 8
Regular octagon
Each internal angle:
135
Sides: 9
Regular nonagon
Each internal angle:
140
Sides: 10
Regular decagon
Each internal angle:
144