formula page for this unit! quiz tomorrow!images.pcmac.org/sisfiles/schools/tn/bradleycounty/... ·...
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Unit 4 (module 2)slope,perimeter,area.notebook
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February 22, 2017
Formula Page for this Unit! Quiz tomorrow!
Slope Formula: riserun
slope intercept form:
slope point form:
distance formula:
Area of triangle?
Area of square?
Area of Rectangle?
Area of parallelogram?
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1. Slope intercept form
2. Distance Formula
3. Slope formula
4. Midpoint Formula
5. Slope/point formula
6. Area of square
7. Area of triangle
8. Area of rectangle
9. Area of parallelogram
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G‐GPE.B.4, 5, 6, & 7 B.4 Use coordinates to prove simple geometric theorems algebraicallyProve the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
B.5
B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
B.7 Use coordinates to compute perimeters of polygons and areas of triangles andrectangles, e.g., using the distance formula.
Module 2: Coordinate Proof Using Slope and DistanceTN Ready Standards
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Theorem: Slope Criteria for Parallel Lines
Two nonvertical lines are parallel if and only if they have the same slope.
Two nonvertical lines are perpendicular if and only if theproduct of their slopes is 1.
What is the slope?
';
* We won't understand this until we know what slope means!
and Perpendicular Lines
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3 ways to find slope!
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There are 4 different kinds of slope. You need to know each by their distinct picture. **Remember you always read graphs from left to right.
Positive
Negative
Horizontal line = zero slope
Undefine Vertical line.
Pull
Pull
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When given a graph find slope by counting rise / run from point to point on the graph.
Pull
Pull
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Find the slope of the line by counting (rise / run) opposite of rise is to fall.
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Find the slope of the line by counting (rise / run).
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When given an equation such as y=mx+bslope is the coefficient to x. (m) ALWAYS!
Pull
Pull
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y = 4x + 6
m = 4
What is the slope of the given equation (function) ?
y = 1/3x 9
m = 1/3
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y = x + 3/4
m = 1
4x + 2y = 164x = 4x + 162y = 4x + 162 2 2y = 2x + 8m = 2
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2x + y = 82x = 2x + 8y = 2x + 8m = 2
y = 2 + 5x
y = 5x 2m = 5
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When given two points from the line, plug them into the slope formula and solve for slope.
m =y2 y1
x2 x1
Find the slope of the line that contains
(5, 2), (1, 4)
Pull
Pull
Click on the star to make it dance. Showing off the formula.
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Find the slope of the line that contains the given points.
(2, 4), (2,4)
(0,2), (2, 0)
(3, 4), (4, 2)
(0, 6), (1, 1)
(1, 9), (3,9)
(5, 7), (5, 1)
Pull
Pull 4 (4)
2 (2)
Pull
Pull
Pull
Pull 9 9
3 1
Pull
Pull
Pull
Pull
Pull
Pull
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How do you find slope if you are given a graph?
How do you find slope if you are given an equation?
What might you have to do to the equation first?
How do you find slope if given two points from the line?
What do the little 2's & 1's mean in the slope formula?
RECAP!
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So if we know what slope is now, how can we determine if two lines are parallel? or perpendicular?
Two nonvertical lines are parallel if and only if they have the same slope.
Two nonvertical lines are perpendicular if and only if theproduct of their slopes is 1.
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What are Parallel and Perpendicular Lines?
Draw an example of each in your notebook.
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Let's take a look at a graph of 2 parallel lines.What do you notice?
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Perpendicular Lines
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Parallel Lines have the same ___________.
How in the world will we remember this?
I KNOW!!
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Parallel Lines have the same slope.Parallel Lines have the same slope.Parallel Lines have the same slope,
and never will they meet.(to the tune of Skip to My Lou)
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What about perpendicular lines?
Slopes of perpendicular lines have NEGATIVE RECIPROCAL
slopes.
Which means... take the slope and flip it, then make it opposite.
m = (1/2)
What is the perpendicular slope?
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Perpen, Perpendicular. Right Angle.Perpen, Perpendicular. Right Angle.
First you take the slope and you flip it, you flip it.Then you take the slope and make it opposite,
opposite.Perpen, Perpendicular. Right Angle.
(to the tune of Peanut Butter and Jelly)
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Write the equation of a line that is PARALLEL to the following:
y=4x+2
y=-2/3x-1
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Write the equation of a line that is PERPENDICULAR to the following:
y=4x+2
y=-2/3x-1
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Write an equation of a line that is parallel to the following and goes through the following point:
y=2/3x + 5 through the point (6,5)
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Wait, how can we do that?Point/Slope form:
go back
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Write the equation of the line that is perpendicular to the line
with the equation below:
y = (1/3) x + 7 and goes through the point (2,3)
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ACT STARTER:
What is the least common multiple of 8, 16, 24 and 48?
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Classifying Quadrilaterals
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Special Quadrilaterals:ParallelogramProperties:
A quadrilateral with both pairs of opposite sides parallel.Opposites sides are congruent.
Consecutive angles are supplementary
Opposite angles are congruent.
Diagonals bisect each other
(Click on each property to have it fly in for effect.)
A B
CD
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Special Quadrilaterals:RectangleProperties:
A parallelogram with four right angles.
Diagonals are congruent.
If only one right angle is marked, the figure is a rectangle.
Has all the properties of a parallelogram.
J K
LM
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:RhombusProperties:
A parallelogram with four congruent sides.
Each diagonal bisects two angles.
Diagonals are perpendicular.
All properties of a parallelogram apply.
E
F
G
H
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:TrapezoidProperties:
A quadrilateral with exactly one pair of parallel sides.
Both pairs of base angles of an isosceles trapezoid are congruent.
The base and one of the legs form the base angles.
The parallel sides are called bases; the nonparallel sides are called legs.
R S
TU
If legs are congruent, then it is an isosceles trapezoid.
Diagonals of an isosceles trapezoid are congruent.
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:SquareProperties:
A parallelogram with four congruent sides and four right angles.
Diagonals are congruent and perpendicular.
Has all the properties of a parallelogram, a rhombus and a rectangle.
Diagonals bisect opposite angles.
Diagonals bisect each other.
N O
PQ
(Click on each property to have it fly in for effect.)
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Special Quadrilaterals:KiteProperties:
A quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent.
Diagonals are perpendicular.
I
T
E
K
(Click on each property to have it fly in for effect.)
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Label
Name the QuadrilateralUse the eraser to reveal the name of the quadrilateral found to
the right of the figure.
Rectangle
Isosceles Trapezoid
Parallelogram
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kite
Properties of Quadrilaterals
Guess the correct answer and pop a balloon.
rhombus square trapezoid
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If you were given the coordinates of a figure and asked toclassify what type of quadrilateral it is, what might you need to know besides slope?
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February 22, 2017Pull
Pull
What is the distance formula and midpoint formula?
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Applying Distance and Midpoint Formulas
The distance d between any two points (x1, y1) and (x2, y2) in a coordinate plane is:
,(x2 y2)
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Ex. 1 Find the distance between (1, 3) and (5, 2).Let (x1, y1) = (1, 3) and (x2, y2) = (5, 2)
This means that the distance between the points is
It doesn't matter which ordered pair is and (x1, y1) (x2, y2)
units
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Ex. 1 Find the distance between (1, 3) and (5, 2).Let (x1, y1) = (1, 3) and (x2, y2) = (5, 2)
This means that the distance between the points is
It doesn't matter which ordered pair is and (x1, y1) (x2, y2)
units
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