Transcript Geometry and Measurement

Geometry and Measurement
What You Will Learn
 To draw a line segment parallel to another line segment
 To draw a line segment perpendicular to another line segment
 To draw a line that divides a line segment in half and is
perpendicular to it
 To divide an angle in half
 To develop and use formulas to calculate the area of triangles
and parallelograms.
 CHALLENGE
 Try to draw what you think the first 5 bullets may look like.
What You Will Need
• Geometry Set
– Ruler
– Protractor
– Right Triangle
• Pencil
• Textbook
Video Support
http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons
Learn Alberta: Working with Angles
Review
Line Segment: the part of a line between 2 end points.
Line: a line segment with no end points
3.1 Parallel and Perpendicular Line Segments
Student Outcome: I can perform geometric constructions.
 After this lesson you will be able to…
 Draw line segments that are parallel to each other
 Draw line segments
that are at right angles to
each other.
What Are Line Segments?
 Parallel Line Segments
 Describes lines in the same plane that never cross, or
intersect
 They are marked using arrows
 The perpendicular distance between
line segments must be the same at
each end of the segment.
 To create, use a ruler and a right triangle, or paper
folding
Parallel sides
Student Outcome: I will be able to describe different shapes
Parallel:
two lines or two sides that are the same distance apart and never meet.
Arrows:
show parallel sides
Vertex:
the point where sides meet or intersect
Learn Alberta
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html
Student Outcome: I will be able to describe different shapes
Parallel:
two lines or two sides that are the same distance apart and never meet.
Arrows:
show parallel sides (where do the arrows go below)?
Vertex:
the point when sides meet or intersect
Learn Alberta - parallel
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html
PAGE 84
• Let’s draw parallel line segments
• Try to draw and check your drawings.
What Are Line Segments?
 Perpendicular Line Segments
 Describes lines that intersect at right angles (90°)
 They are marked using a small square
 To create use a ruler and a protractor,
or paper folding.
Student Outcome: I will be able to describe different shapes
Perpendicular: where a horizontal edge and vertical edge intersect to form a right angle
OR
when two sides of any shape intersect to make a right angle
Right Angle: 90’ symbol is a box in the corner
Perpendicular side
Vertical side
Perpendicular side
Learn Alberta - Perpendicular
http://www.learnalberta.ca/content/memg/index.html?term=Division02/Perpendicular/index.html
Student Outcome: I will be able to describe different shapes
Perpendicular: where a horizontal edge and vertical edge intersect to form a right angle
OR
when two sides of any shape intersect to make a right angle
Right Angle: 90’ symbol is a box in the corner
How many perpendiculars do you see in each diagram
Student Outcome: I will be able to describe different shapes
Perpendicular: where a horizontal edge and vertical edge intersect to form a right angle
Right Angle: 90’ symbol is a box in the corner
How do you describe a perpendicular using points
OnYour Own…
 What are 5 examples of parallel line segments
in the real world?
 What are 5 examples or perpendicular line
segments?
PAGE 85
• Let’s us draw perpendicular line segments
• Try to draw and check your drawings.
Practice
 Pg 87. #5
 What are the parallel and perpendicular line
segments in the painting.
Practice
 Pg 87. #5
 What are the parallel and perpendicular line
segments in the painting.
 Segments CD, EF, and GH
are parallel.
 AB is perpendicular to CD,
EF, and GH.
Practice
 Identify the parallel and perpendicular streets
in the diagram.
Practice
 Identify the parallel and perpendicular streets
in the diagram.
Major Street and Centre
Street are parallel
Main Street and North Street
are parallel.
Major Street is perpendicular
to Main Street and North
Street.
Centre Street is perpendicular to Main Street
and North Street.
On Your Own…
• Assignment Page 86-88
2,12,13,14,15,
11
1,2,7,8,12,13,
1,2,5,7,9,
Airport Final Design
(minimum requirements)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Four Sets of Parallel lines.(Runways – 1cm wide, Taxi Lanes – 0.3cm wide)
One perpendicular.
One perpendicular bisector
One angle bisector.
One parallelogram.
One triangle.
One Circle
Buildings
Colored
Straight lines
Pencil
Creativity
Parent Signature
(area, radius, diameter)
(Terminal, Maintenance, Control Tower)
MATH LINK PAGE 88
Parallel and Perpendicular Line Segments
Figure 1. Airport diagram of Boston’s Logan International Airport with
Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights
(in red).
3.2
Draw Perpendicular Bisectors
Student Outcome:
I will understand and be able to draw a perpendicular bisector.
 3 Ways
 A) folding paper
 B) protractor and ruler
 C) compass
Student Outcome: I will understand and be able to draw a
perpendicular bisector.
 On your paper:
 Use a ruler to draw a 6 cm line segment
 Label the endpoints A and B.
 Fold the piece of paper so that the points A and B lie
on top of each other.
 Use a ruler to draw a line segment on the crease. Label
this line segment CD. Label the point where the two
line segments intersect P.
 Use a ruler to measure lengths AP and BP. What do
you notice?
 Use a protractor to measure the 4 angles made by the
intersecting line segments. What do you notice about
these angles.
Student Outcome: I will understand and be able to draw a
perpendicular bisector.
• A Perpendicular Bisector:
– cuts a line segment in half and is at right angles
(90°) to the line segment.
– If line segment AB is 2
20cm long where
is the perpendicular
bisector?
• Pg. 93, #9
Example
• In some First Nations communities, fish are dried on a
drying rack like the one shown. An extra support is
needed for this drying rack to hold all the salmon that
were caught. Use what you know about drawing
perpendicular bisectors to explain how to do this. Include
the lengths shown
in the picture in
your explanation
Solution
• Cut a support post that is 1.4 m long. To find the halfway
point of the top horizontal pole, divide the length of 3 m
in half to get 1.5 m. Place the support at this halfway
point. Measure a right angle where the top pole and the
support meet in
order to position
the support
perpendicular to
the top pole.
Let’s Practice
Page 92-93
 #4- Trace the lines onto your paper. Use your
protractor to measure the correct angles
2, 5, 6, 7, 10
8
2, 4, 5, 6, 7
1, 2, 3, 4, 5,
MATH LINK PAGE 93
Perpendicular Bisector
Show Me What You Know #1
On a piece of paper
1. Draw one set of parallel lines 7cm long
(on the front)
2. Draw a 8cm line segment with a 6cm perpendicular on it.
(on the back)
All About Angles
http://www.freewebs.com/mrsdeleon/mathlinks.htm#Geometry
Virtual Protractor
Kidport – Measuring Angles
3.3 Drawing Angle Bisectors
Student Outcome:
I will understand and be able to draw a angle bisector.
 3 Ways
 A) folding paper
 B) protractor and ruler
 C) compass
Student Outcome: I will understand and be able to draw an
angle bisector.
 An angle bisector is a line that divides the
angle evenly in terms of degrees.
D
45’
<ABD = 45’
What is
<DBC =
Student Outcome: I will understand and be able to draw an
angle bisector.
 To draw a line that divides a line segment in
half and is perpendicular to it
 To divide an angle in half
PAGE 95
• Let’s draw angle bisectors
• Try to draw and check your drawings.
On Your Own…
• Page 97-99
3, 5, 12, 13, 15
8
3, 5, 6, 9, 12
1, 3, 5, 6, 7,
MATH LINK PAGE 99
Angle Bisector
Review
Student Outcome: I will be able to understand perimeter.
How much fence will you need to enclose this baseball field?
Review
Student Outcome: I will be able to understand perimeter.
Perimeter: the distance around a shape
or
the sum of all the sides
Review
Student Outcome: I will be able to understand perimeter.
How can you figure out these perimeters?
Review
Student Outcome: I will be able to understand area.
You need a tarp to cover this soccer field. How do you figure this out?
Review
Student Outcome I will be able to understand area.
Area: the amount of surface a shape covers
: it is 2-dimensional - length (l) and width (w)
: measured in square units (cm ²) or (m²)
Review
Student Outcome: I will be able to understand area.
46 cm
Figure the area for these objects?
8 cm
50 cm
183 cm
6cm
100 cm
Review
Student Outcome: I will be able to understand perimeter.
46 cm
Figure the perimeter for these objects?
50 cm
8 cm
183 cm
6cm
100 cm
Geo Boards for Proof
Student Outcome: I will be able to model area and perimeter
What are the perimeters
for each rectangle?
Length
Width
Area
Perimeter
What are the areas for
each rectangle?
What do you notice?
Geo Boards for Proof
Student Outcome: I will be able to model area and perimeter
8 cm²
14cm²
18cm²
20cm²
Length
Width
What interpretations can you make based on the chart above?
The rectangles with the least width has the least area.
The rectangle closest in shape to a square has the greatest area.
Area
Perimeter
Geo Boards for Proof
Student Outcome: I will be able to model area and perimeter
8 cm²
14cm²
18cm²
20cm²
Length
Width
Area
Perimeter
8
1
8
18
7
2
14
18
6
3
18
18
5
4
20
18
What interpretations can you make based on the chart above?
The rectangles with the least width has the least area.
The rectangle closest in shape to a square has the greatest area.
Changing Garden
Area and Perimeter Video ( Learn Alberta)
http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=12
Area and Perimeter of your Foot
Show Me What You Know #2
On a piece of paper
1. Draw a 60’ angle. Then bisect it.(on the front)
2. Draw a 8cm line segment with end points labeled A and B.
Then draw the perpendicular bisector on it with an endpoint
labeled C(on the back)
3.4 Area of Parallelogram
PAGE 100
Student Outcome: I will be able to solve the area of a parallelogram.
• Let’s build a parallelogram
• What is the relationship between base (b) and
height (h)?
Area of a rectangle or square
Area = length x width
A=lxw
Area of a parallelogram
Area = base x height
A=bxh
Let’s Practice
• Page 105
• 3a.
• 3b.
Let’s Practice
• Page 105
• 4a.
• 4b.
On Your Own…
• Page 104-107
2, 7, 12, 16, 17
9
2, 3, 7, 12, 13
1, 3, 5, 7, 8,
MATH LINK PAGE 107
Parallelogram
Show Me What You Know #3
• Answer the following questions
1.
2.
Use White Board Grids to Draw
Parallelograms
fgdd
Groupings: 1-6a and 5-8
3.5 Area of Triangle
PAGE 108
Student Outcome: I will be able to solve the area of a triangle.
• Let’s build a triangle
• What is the relationship between base (b)
height (h) and area?
Area of a triangle
Area = (base x height) ÷ 2
Area = (b x h) ÷ 2
Let’s Practice
• Page 113
• 4a.
5a.
• 4b.
5b.
On Your Own…
• Page 114
Practice and Apply #9, 10, 12, 14, 15,
Extend #16, 17, 19
MATH LINK PAGE 115
Triangle
Show Me What You Know #4
• Answer the following questions
1.
2.
Show Me What You Know #5
On a piece of paper
1. Draw a parallelogram with a height of 3cm and a base of 8cm.
Solve the area.(on the front)
2. Draw a triangle with a base of 6cm and a height of 5cm.
Solve the area.(on the back)
3.5 Area of a Circle
AC DR
Area Circumference Diameter
Radius
Construct Circles (Unit 8)
Student outcome: I will be able to describe the relationship of radius, diameter and
circumference
Use your compass to draw a circle…Use a ruler to find your radius first!
Radius
Distance from the
centre of the circle
to the outside
edge…represented
by “r”
Diameter
Distance across a
circle through its
centre…represented
by “d”
Construct Circles (Unit 8)
Student Outcome: I will be able to describe the relationship between radius, diameter
and circumference
Question…
• How can you find the diameter if you are given the
radius?
d=rx2
Construct Circles (Unit 8)
Student Outcome: I will be able to describe the relationship between radius, diameter
Question…
• How can you find the radius if you are given the
diameter?
r=d÷2
Area of a Circle
Area means the total amount of space
inside of a circle (or any shape).
Try to come up with an equation
for a circle using the hints given...
5m
What are the hints?
•
•
•
•
•
•
Area of a Circle
Area Equation is…
5m
Answer is…there are roughly
3 squares (l x w) that fit into a
circles. The remaining area
outside of the circles roughly
make up the area in the 4th
part of the circle.
Actual Area Equation:
Area = ∏r ²
Area of a Circle
Student outcome: I will be able to solve the area of a circle.
Radius
6 cm
8 cm
14 cm
Estimate Area
Actual Area
A=3xrxr
or
A = 3r² A = ∏r² or A = ∏ x r x r
Area of a Circle
Student outcome: I will be able to solve the area of a circle.
Show all your work...complete one step at a time!
Diameter
6 cm
10 cm
13 cm
Find the
Estimate Area
Actual Area
“_________” A = 3r² or A = 3xrxr A= ∏r² or A = ∏xrxr
Activity
Quick Draw
(see handout)
On Your Own…
• CHAPTER REVIEW
• Page 116-117 #1-17
Airport Final Design
(minimum requirements)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Four Sets of Parallel lines.(Runways – 1cm wide, Taxi Lanes – 0.3cm wide)
One perpendicular.
One perpendicular bisector
One angle bisector.
One parallelogram.
One triangle.
One Circle
Buildings
Colored
Straight lines
Pencil
Creativity
Parent Signature
(area, radius, diameter)
(Terminal, Maintenance, Control Tower)
LET’S BUILD
LET’S BUILD
http://www.calfeedesign.com/framemeasurement.htm
http://mtobikes.com/mountain-bike-frame-geometry/