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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 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/