Download Parallel and Perpendicular Lines IM1 November 09, 2015

Parallel and Perpendicular Lines
BIG PICTURE of this UNIT:
November 09, 2015
• mastery with algebraic skills to be used in our work with
co-ordinate geometry (midpoint, length, slope)
• understanding various geometric properties of
quadrilaterals & triangles
• how do you really prove that something is “true”?
Where we’ve been Where we are
You know about
geometric figures
CONTEXT of this LESSON:
and now you know
how to find a
midpoint and
length
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Becoming proficient
with another
analytical tool that
we can use in coordinate geometry:
parallel and
perpendicular lines
Where we are
heading
How can I prove
various geometric
properties of
quadrilaterals and
triangles?
Parallel and Perpendicular Lines
Lesson Objectives:
1.
2.
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Exploring parallel lines and their proper3es.
Exploring perpendicular lines and their proper3es. November 09, 2015
Parallel and Perpendicular Lines
November 09, 2015
Warm-up
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1.
Solve the following equation for x.
2.
Determine the midpoint and length of the line segment
formed between (2, 3), and (-8, 9). Draw a picture!
Parallel and Perpendicular Lines
November 09, 2015
We are going to use the GeoGebra App (search GeoGebra in your web
browser to explore parallel and perpendicular.
Click "Algebra" once you are in the App.
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Parallel and Perpendicular Lines
November 09, 2015
Pick two points A and B Record the points in the table below Draw a line segment between them and determine the slope of the line segment between those points. Now Find another two points that create a PARALLEL line to the one you just made. Do this 6 different 3mes Point A
Point B
Slope of
AB
Point C
Point D
Slope of
CD
Observations:
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Parallel and Perpendicular Lines
November 09, 2015
Given the three points A, B, C… I want you to find the fourth point D such that line segment AB is Parallel to line segment CD
Point A
(2,5)
(3,6)
(-5,-4)
(-2,-8)
(3,7)
(-2,9)
(0,-7)
Point B
(4,7)
(0,-2)
(7,-1)
(-8,6)
(-4,2)
(-6,2)
(5,0)
Point C
(-3,-2)
(1,1)
(0,5)
(0,0)
(-2,1)
(5,0)
(2,3)
Point D
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Parallel and Perpendicular Lines
November 09, 2015
Exploring Perpendicularism using dynamic geometry so5ware: GeoGebra
Define perpendicular in your own words:
Draw a picture of perpendicular lines:
Draw 4 shapes that you KNOW have perpendicular lines:
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Parallel and Perpendicular Lines
November 09, 2015
Pick two points A and B. Record the points in the table below. Draw a line segment between them and determine the slope of the line segment between those points. Now Find another two points that create a perpendicular line to the one you just made. Do this 6 different 3mes. Do your best to “eyeball” it…get as close as you can. Determine the slope of the new perpendicular line segment. Point A
Point B
Slope of
AB
Point C
Point D
Slope of
CD
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Parallel and Perpendicular Lines
November 09, 2015
The following points AB and CD WILL create perpendicular line segments. Explore the three examples in GeoGebra and see what you can determine about perpendicular lines and their slopes. Point A
(1,1)
(-3,-1)
(-2,3)
Point B
(5,2)
(-1,3)
(2,-2)
Point C
(2,4)
(-5,3)
(-2,-3)
Point D
(3,0)
(3,-1)
(3,1)
Slope of
AB
Slope of
CD
Observations:
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Parallel and Perpendicular Lines
November 09, 2015
Given the points A(2,3) B(5,8) C(10,5) and D(7,0) create the line segments AB, BC, CD, DA and then discuss what kind of shape this makes. Can you be certain of the shape that it makes? Could you prove your ideas? Draw a picture of your GeoGebra below. IM1