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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 the what you think the first 5 bullets may
look like.
What You Will Need
• Geometry Set– Ruler– Protractor – Right Triangle
• Pencil• Textbook
ReviewLine 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 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
Lesson 1Students will be able to describe different shapes
Learn Albertahttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html
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
Lesson 1Students will be able to describe different shapes
Learn Alberta - parallelhttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html
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
PAGE 84
• Let’s us 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.
Perpendicular: where a horizontal edge and vertical edge intersect to form a right angleOR
when two sides of any shape intersect to make a right angle
Right Angle: 90’ symbol is a box in the corner
Vertical
Horizontal
Learn Alberta - Perpendicularhttp://www.learnalberta.ca/content/memg/index.html?term=Division02/Perpendicular/index.html
Vertical side
Perpendicular side
Perpendicular side
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
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 CentreStreet are parallel Main Street and North Streetare parallel. Major Street is perpendicularto Main Street and NorthStreet. Centre Street is perpendicular to Main Street and North Street.
On Your Own…
• Page 87
Practice and Apply #7, 9, 10, 12, 13, Extend #15, 16
3.2Draw Perpendicular Bisectors
What is A Perpendicular Bisector? On your rice paper:
Use a ruler to draw a 15 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.
What is a Perpendicular Bisector??
• A Perpendicular Bisector:– Is a line segment in half and is at right angles (90°)
to the line segment.
Example• Pg. 93, #9• 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 PracticePg. 92 #4- Trace the lines onto your rice paper. Use your
protractor to measure the correct angles #6, 7, 8, 10
Due Tomorrow for Homework!!
3.3 Draw Angle Bisectors
3.3 Draw Angle Bisectors
http://www.freewebs.com/mrsdeleon/mathlinks.htm#Geometry
What Will I Learn??
To draw a line that divides a line segment in half and is perpendicular to it
To divide an angle in half
Lesson #3Student Outcome: I will be able to understand perimeter.
How much fence will you need to enclose this baseball field?
Lesson #3Student Outcome: I will be able to understand perimeter.
Perimeter: the distance around a shape
or
the sum of all the sides
Lesson #3Student Outcome: I will be able to understand perimeter.
How can you figure out these perimeters?
Lesson #3Student Outcome: I will be able to understand perimeter.
You need a tarp to cover this soccer field. How do you figure this out?
Lesson #3Student Outcome I will be able to understand perimeter and 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)
Lesson #3Student Outcome: I will be able to understand perimeter and area.
Figure the area for these objects?
6cm
8 cm50 cm
100 cm
46 cm
183 cm
Lesson #3Student Outcome: I will be able to understand perimeter and area.
Figure the perimeter for these objects?
6cm
8 cm50 cm
100 cm
46 cm
183 cm
Lesson #3Student Outcome: I will be able
to understand perimeterand area.
What are the perimeters for each rectangle?
What are the areas for each rectangle?
What do you notice?
Length Width Area Perimeter
Page 128
Lesson #3Student Outcome: I will be able
to understand perimeter and area.
Page 129
Length Width Area Perimeter
8 cm²
14cm² 18cm² 20cm²
What did we find out?
Lesson #3Student Outcome: I will be able
to understand perimeter and area.
Page 129
Length Width Area Perimeter
8 cm²
14cm² 18cm² 20cm²
What did we find out?
The rectangles with the least width has the least area.
The rectangle closest in shape to a square has the greatest area.
Lesson #3Student Outcome: Student Outcome: I will be able to understand perimeter and area.
http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=12
Area and Perimeter Video ( Learn Alberta)
What is an Angle Bisector??
An angle bisector is a line that divides the angle evenly in terms of degrees.
The perimeter of a polygon is the distance around the outside of the polygon. A polygon is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units. To help us make this distinction, look at our picture of a rectangular backyard. The yard is 2-dimensional: it has a length and a width. The amount of fence needed to enclose the backyard (perimeter) is 1-dimensional. The perimeter of this yard is the distance around the outside of the yard, indicated by the red arrow; It is measured in linear units such as feet or meters.
PERIMETER
To find the perimeter of a polygon, take the sum of the length of each side. The polygons below are much smaller than a fenced-in yard. Thus, we use smaller units in our examples, such as centimeters.
Area of a rectangle or square
Area = length x width
A = l x w
Area of a parallelogram
Area = base x height
A = b x h
Area of a triangle
Area = (base x height) ÷ 2
Area = (b x h) ÷ 2
http://www.calfeedesign.com/index.htm
http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Bicycle_Frame_Diagram-en.svg/443px-Bicycle_Frame_Diagram-en.svg.png