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# Geometry and Measurement - PowerPoint PPT Presentation

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

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## PowerPoint Slideshow about ' Geometry and Measurement' - tynice

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### Geometry and Measurement

• 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.

• Geometry Set

• Ruler

• Protractor

• Right Triangle

• Pencil

• Textbook

http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons

Learn Alberta: Working with Angles

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 SegmentsStudent 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.

• 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: 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

Student Outcome: I will be able to describe different shapes

Learn Alberta

http://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

Student Outcome: I will be able to describe different shapes

Learn Alberta - parallel

http://www.learnalberta.ca/content/memg/index.html?term=Division02/Parallel/index.html

• Let’s us draw parallel line segments

• Try to draw and check your drawings.

• 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 angle

OR

when two sides of any shape intersect to make a right angle

Right Angle: 90’ symbol is a box in the corner

Vertical

Perpendicular side

Vertical side

Student Outcome: I will be able to describe different shapes

Perpendicular side

Horizontal

Learn Alberta - Perpendicular

http://www.learnalberta.ca/content/memg/index.html?term=Division02/Perpendicular/index.html

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

Student Outcome: I will be able to describe different shapes

• What are 5 examples of parallel line segments in the real world?

• What are 5 examples or perpendicular line segments?

• Let’s us draw perpendicular line segments

• Try to draw and check your drawings.

• Pg 87. #5

• What are the parallel and perpendicular line segments in the painting.

• 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.

• Identify the parallel and perpendicular streets in the diagram.

• 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.

• Page 87

Practice and Apply #7, 9, 10, 12, 13,

Extend #15, 16

Airport Final Design(minimum requirements)

• 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.

7. Buildings (Terminal, Maintenance, Control Tower)

8. Colored

9. Straight lines

10. Pencil

11. Creativity

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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Draw Perpendicular Bisectors

Student Outcome: Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). I will understand and be able to draw a perpendicular bisector.

• 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: Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). 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?

Example Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• 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

Solution Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• 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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Page 92

• #4- Trace the lines onto your paper. Use your protractor to measure the correct angles

• #6, 7, 8,

• Due Tomorrow for Homework!!

MATH LINK PAGE 93 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Perpendicular Bisector

### Practical Quiz #1 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

On a piece of paper

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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Angles

Virtual Protractor

Kidport – Measuring Angles

### 3.3 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Drawing Angle Bisectors

Student Outcome: Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). 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.

<ABD = 45’

What is

<DAC =

D

45’

Student Outcome: Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). 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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Let’s draw angle bisectors

• Try to draw and check your drawings.

On Your Own… Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Page 98

Practice and Apply #6, 7, 8, 9, 12,

Extend #13,14, 15

MATH LINK PAGE 99 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Angle Bisector

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

How much fence will you need to enclose this baseball field?

Student Outcome: I will be able to understand perimeter.

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Perimeter: the distancearound a shape

or

the sum of all the sides

Student Outcome: I will be able to understand perimeter.

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

How can you figure out these perimeters?

Student Outcome: I will be able to understand perimeter.

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

You need a tarp to cover this soccer field. How do you figure this out?

Student Outcome: I will be able to understand area.

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

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)

Student Outcome I will be able to understand area.

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

46 cm

Figure the area for these objects?

50 cm

8 cm

Student Outcome: I will be able to understand area.

183 cm

6cm

100 cm

### Review Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

46 cm

Figure the perimeter for these objects?

50 cm

8 cm

Student Outcome: I will be able to understand perimeter.

183 cm

6cm

100 cm

Geo Boards for Proof Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Student Outcome: I will be able to model area and perimeter

What are the perimeters for each rectangle?

What are the areas for each rectangle?

What do you notice?

Geo Boards for Proof Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Student Outcome: I will be able to model area and perimeter

8 cm²

14cm²

18cm²

20cm²

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.

Geo Boards for Proof Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Student Outcome: I will be able to model area and perimeter

8 cm²

14cm²

18cm²

20cm²

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 and Perimeter Video ( Learn Alberta) Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

http://www.learnalberta.ca/content/me5l/html/math5.html?goLesson=12

### Practical Quiz #2 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

On a piece of paper

Draw a 60’ angle. Then bisect it.(on the front)

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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Area of Parallelogram

PAGE 100 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). 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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Area = length x width

A = l x w

Area of a parallelogram

Area = base x height

A = b x h

Let’s Practice Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Page 105

• 3a.

• 3b.

Let’s Practice Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Page 105

• 4a.

• 4b.

On Your Own… Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Page 105

Practice and Apply #7, 9, 10, 12, 13, 14,

16, 17

Extend #19, 20

MATH LINK PAGE 107 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Parallelogram

### 3.5 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Area of Triangle

PAGE 108 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). 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 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

Area = (base x height) ÷ 2

Area = (b x h) ÷ 2

Let’s Practice Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Page 113

• 4a. 5a.

• 4b. 5b.

On Your Own… Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• Page 114

Practice and Apply #9, 10, 12, 14, 15,

Extend #16, 17, 19

MATH LINK PAGE 115 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Triangle

### Practical Quiz #3 Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

On a piece of paper

Draw a parallelogram with a height of 3cm and a base of 8cm. Solve the area.(on the front)

Draw a triangle with a base of 6cm and a height of 5cm. Solve the area.(on the back)

On Your Own… Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

• CHAPTER REVIEW

• Page 116-117 #1-17

Airport Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red). Final Design(minimum requirements)

• 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.

7. Buildings (Terminal, Maintenance, Control Tower)

8. Colored

9. Straight lines

10. Pencil

11. Creativity

LET’S BUILD Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

LET’S BUILD Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

http://www.calfeedesign.com/framemeasurement.htm Airport with Runway Intersection Lights, Takeoff Hold Lights, and Runway Entrance Lights (in red).

http://mtobikes.com/mountain-bike-frame-geometry/