3. Angles and Triangles

Class: Technical Graphics - Year 1

Learning Intentions and Success Criteria

Textbook References:

JCTG: Junior Certificate Technical Graphics (O’Callaghan)

UTG: Understanding Technical Graphics (O’Sullivan)

WS: Worksheets

Specialist equipment required for class

• H and 2H pencil

• Pencil sharpener, eraser, colouring pencils

• 45, 30 and 60 degree set-squares

• Compass

• Drawing clips or masking tape

• Protractor

• A3 Folder

• Textbook: Understanding Technical Graphics

• iPad

Equipment required at home (later in the year)

• T-square

• Drawing Board

• Internet connection and access to SharePoint

Scheme for this topic

• In pairs, answer the following questions:

Keywords

• Vertical and vertically

• Horizontal and horizontally

• Increment

• Measure

• Construction

• Perpendicular

• Parallel

• Produce

• Diagram

• Protractor

• Iarnród

• Éireann

• Acute

• Angle

• Obtuse

• Reflex

• Complementary

• Supplementary

• Opposite

• Example

• Corresponding

• Alternate

• Envelope

• Inclined

• Staple

• Picnic

• Vertex

• Pylon

• Offset

Sheets

Read about angles and the protractor on page 17 of your textbook
Complete the worksheet on measuring angles below using your protractor

Sheet 5 (Road sign and EA Games Logo: UTG, page 12 and 13)

• Fill in your name, SHEET 5: INCLINED LINES 1 and the date

• Measure 30mm vertically and draw a light construction line across the page with your T-square(This is your base line)

• Measure 80mm horizontally and draw a light construction line vertically with your Set-square

• This will give you the bottom left corner of your diagram (Road sign, Exercise 2 on Page 12 of your textbook)

• Measure 245mm along the horizontal line and draw a vertical line with your Set Square

• Measure 50mm along the vertical line and draw a horizontal line with your T-square to form a rectangle

• Measure along the horizontal line and mark off the measurements shown in the diagram, Exercise 2 on Page 12 of your textbook

• Draw light construction lines through these marks with your 45 degree Set-Square

• Looking at the diagram on page 12 of your textbook, draw thick lines over the construction lines using your Set-squares

• From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.

• Write ROAD SIGN between these guidelines

• From the top of the Road Sign diagram, measure vertically 40mm and draw a horizontal line

• Measure 80mm horizontally and draw a light construction line vertically with your Set-square

• This will give you the bottom left corner of your diagram (EA Games logo, Exercise 6 on Page 13 of your textbook)

• Measure along the horizontal line and mark off the measurements shown in the diagram in Exercise 6

• Draw light construction lines with your 30/60 degree Set-Square through these marks (at 60 degrees!!!)

• Measure 110mm along the vertical line and draw a horizontal line with your T-square

• Measure along the vertical line and mark off the measurements shown in the diagram, Exercise 6 on Page 13 of your textbook

• You will only be able to draw some of the diagram. Use your 30/60 degree Set-square to complete the diagram at the end

• From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.

• Write EA GAMES between these guidelines

Sheet 6 (NIKE Logo: UTG, page 16

• Fill in your name, SHEET 6: INCLINED LINES 2 and the date

• Measure 80mm vertically and draw a light construction line across the page with your T-square (This is your base line)

• Measure 100mm horizontally along the base line and draw a vertical line, this is the bottom left corner of your NIKE logo

• Mark the distances along this vertical line as shown on Exercise 2 on page 16 of your text book

• Mark the distances along the base line as shown on Exercise 2 on page 16 of your text book

• Looking at the diagram for Exercise 2 on page 16 of your textbook you will notice the angle of the NIKE logo is 75 degrees

How can this angle be drawn with Set-squares?

• Rest the 45 degree Set-square on top of the 30 degree end of the 30/60 Set-square

• Carefully balance the two Set-Squares and Slide them until they touch the distances you marked on the base line

• Draw light construction lines through these marks with your two Set-Squares

• Many of the lines in this diagram are parallel to each other

• Looking at the diagram on page 12 of your textbook, draw thick lines over the construction lines using your Set-squares to outline the NIKE logo

• From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.

Write NIKE between these guidelines

Sheet 7 (McMahon and Ulster Bank logos, pg 12/13)

Fill in your name, SHEET 7: INCLINED LINES 3 and the date
Measure 60mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 30mm horizontally along the base line and draw a vertical line, this is the bottom left corner of your McMahon logo
Examine the diagram in Question 4 on page 12, plan out how you will draw this object.
Mark out the overall width of the logo (150mm) along your base line.
Mark off the other measurements along this base line. Draw vertical construction lines through these points.
On the first vertical line, measure up 60 and mark it. From this point draw a line at 45 degrees.
Using your 45 degree Set-square follow the diagram to draw the other lines.
Once you are finished the diagram, measure down 10mm, then 5mm more and draw a light construction line. These are the guidelines to write MCMAHON LOGO
Measure 60mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 20mm horizontally along the base line from the Right hand side of the McMahon Logo and draw a vertical line, this is the bottom left corner of your Ulster Bank logo
Examine the diagram in Question 5 on page 13, plan out how you will draw this object.
From both ends of this line draw two lines at 60 degrees and 120 degrees with your 60/30 degree Set-square
Mark off the other measurements along this base line. What should the distance between the construction lines be? Draw construction lines through these points with your 60/30 degree Set-square.
Make sure you draw all light construction lines first. You can then go over the lines again a little heavier to get the Ulster Bank Logo
Once you are finished the diagram, measure down 10mm, then 5mm more and draw a light construction line. These are the guidelines to write ULSTER BANK

Sheet 8 (Pillar, Envelope: pg15, Staple Gun: p16)

Fill in your name, SHEET 8: INCLINED LINES 4 and the date
Measure 25mm vertically and draw a light construction line a quarter of the way across the page with your T-square (This is your base line)
Measure 20mm horizontally along the base line and draw a vertical line, this is the bottom left corner of your Envelope in Exercise 1 on page 15
Draw the outline shape of the envelope.
Follow the instructions on top of page 15. Place one set-square on top of another and draw the lines at angles of 15 and 75 degrees.
When you have finished drawing the envelope, measure 20mm vertically upwards from the top of the envelope. Draw a light horizontal line a quarter ways across the page.
Measure 60mm in from the margin along this line. Draw a vertical line. This is the bottom left corner of the brickwork in the pillar. Draw the pillar shown in Exercise 1.
When you are finished you will have drawn a pillar and an envelop on the left side of the sheet. You will now draw the staple gun on page 16 on the other side of the sheet.
From the top right corner of the envelope draw a light construction line, with the T-Square across the rest of the page
Measure 20mm along this line and draw a vertical line. This is the bottom left corner of the Staple Gun drawn on page 16
Mark the measurements along the horizontal line. Then mark the measurements along the vertical line.
Place one Set-square on top of the other to draw the lines at angels of 15 and 75 degrees. Draw light lines first, then the heavier object lines as you need them.

Sheet 9 (Picnic Table: p17)

Fill in your name, SHEET 9: INCLINED LINES 5 and the date
Measure 60mm vertically and draw a light construction line a quarter of the way across the page with your T-square (This is your base line)
Mark the point 120mm horizontally along the base line from the margin, this is the bottom left corner of first leg of the Picnic Table in Exercise 1 on page 17
Mark the other distances along the base line.
Line up the bottom line of the protractor with the base line at this point. Mark 65 degrees using the protractor.
Join this 65 degree mark to the central point you used with the projector. This is the edge of the first leg of the table.
Mark the point 20mm along the base line. This is the other edge of the first leg. Line the protractor up with this point and the horizontal line.
Use the protractor again and mark 65 degrees. Join this point back to the central point from a moment ago. This will give you both edges of the left leg of the picnic table.
Repeat the procedure to draw the other leg. (HINT: what is 180-65? you will need this to draw the other leg)
Draw the horizontal lines and complete the table as shown in the diagram.
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write PICNIC TABLE between these guidelines

Sheet 10 (Boyne Cable Bridge, pg18) [You will need your PROTRACTOR to complete this drawing]

For this exercise you need your protractor and to familarise yourself with the instructions on Page 17
Fill in your name, SHEET 10: ANGLES 1 and the date
Examine the diagram in Exercise 2 on page 18
Measure 70mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 35mm horizontally along the base line and draw a vertical line, this is the bottom left corner of the roadway of the Boyne Bridge
Measure in 15mm and draw a light vertical line downward, this will give you the left side of the first leg (support) of the bridge
Measure another 10mm horizontally and draw a vertical line, this is the other side of the left leg (support) of the bridge
Measure 20mm vertically downward along this line and draw a horizontal line. This is the bottom of the the first leg.
Measure vertically 10mm upwards from the base line this will give you the top of the roadway of the bridge.
Mark off the position of cables along this line as shown in the diagram in your textbook
Draw the main support for the bridge vertically with your set square
Now use you projector to get the angles you need. Place the centre of the protractor at the base of each cable, mark off the angle required. Draw light lines first then draw over them heavy when you are finished
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write BOYNE BRIDGE between these guidelines

Sheet 11 (Pylon, pg18)

For this exercise you need your protractor and to familarise yourself with the instructions on Page 17
Fill in your name, SHEET 11: ANGLES 2 and the date
Examine the diagram in Exercise 2 on page 18
Measure 30mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 130mm horizontally along the base line and mark the point, this is the bottom left corner of the Pylon
Measure 130mm further, this is the bottom right of the pylon
Measure 75mm vertically upwards, and draw a horizontal line. This should be a light line and there is no particular start and end point
From the bottom corners of the pylon, use your protractor to mark off 35 degrees as shown in your textbook. Draw lines from the bottom left and right corners of the pylon at 35 degrees until they cross the horizontal line 75mm above the base line.
Join these points of intersection back to the bottom corners. Extend these lines upward. These lines are the left and right sides of the pylon.
Use the protractor to mark off the angles shown in your textbook. Make sure that your protractor is always resting on a horizontal line.
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write PYLON between these guidelines

Sheet 12 (Tent Pg:19)

For this exercise you need your protractor and to familarise yourself with the instructions on Page 19
Fill in your name, SHEET 12: ANGLES 3 and the date
Examine the diagram in Exercise 4 on page 19
Measure 50mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 75mm horizontally along the base line and mark the point, this is the bottom left corner of the tent
Along the base line mark the points and lines shown in the diagram
Place the protractor at the bottom left and right of the tent and mark 52 degrees. Draw lines from the bottom corners through the points marked from the protractor. Where they join will give you the top of the tent.
Draw the flag
Next draw the tent opening.
Draw a horizontal line from the top of the tent opening, this will be the top of the window. Mark 10mm in from the top of the opening as shown in the diagram and draw a vertical line, this is the right of the window.
Draw a line across from the top of the side of the tent. This is the bottom of the window. Now try to complete the square!
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write TENT between these guidelines

Sheet 13 (Iarnrod Eireann Logo Pg:19)

For this exercise you need your protractor and to familarise yourself with the instructions on Page 19
Fill in your name, SHEET 13: ANGLES 4 and the date
Examine the diagram in Exercise 5 on page 19
Measure 50mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 190mm horizontally along the base line and mark the point, this is the bottom left corner of the logo
From the bottom point put two set-squares together to get 75 degrees draw the line as indicated in the diagram
From the bottom point draw a line at 45 degrees as indicated in the diagram
From the bottom point of the logo measure 90mm horizontally to the left as shown in the diagram. Draw a line from the point at 75 degrees.
Find the point where this line and the 45 degree line intersect. Draw a horizontal point through this point
Offset horizontal lines from this line as shown in the diagram. NB the measurements are taken vertically, not at an angle!
Use your compass to mark the missing distances.
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write IARNROD EIREANN between these guidelines

Sheet 14 (Umbro Logo, Turn Signals, pg22)

For this exercise you need your protractor and to familarise yourself with the instructions on Page 19
Fill in your name, SHEET 14: ANGLES 5 and the date
Examine the diagram in Exercise 1 on page 22
Measure 60mm vertically down from the top margin and draw a light construction line across the page with your T-square (This is your centre line of the diagram)
Measure 90mm horizontally along the base line and mark the point, this is the left corner of the logo.
Mark off the , 20mm, 20mm, 20mm and the overall length of 200mm along the centre line.
You need to mark off the angle, what is the angle from the centre line?
Mark this angle with the protractor. Repeat for each line. Mirror your lines from the left side and right side, from the top to the bottom.
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write UMBREO LOGO between these guidelines
Examine the diagram in Exercise 2 on page 22
Measure 70mm vertically down from the centre of the Umbro logo and draw a light construction line across the page with your T-square (This is your centre line of the diagram)
Measure 20mm (half 40mm) horizontally each way along the base line and mark the point, draw vertical lines through these points, these are one end of the arrows.
Mark off the 50mm and draw vertical lines through these points. Then measure 60mm from these points and mark the other end of the arrows.
You need to mark off the angle, what is the angle from the centre line?
Mark this angle with the protractor.
Draw the outline of the arrows.
Mirror your lines from the top to the bottom.
The inside arrow is 10mm from the outside arrow. NB: Remember the 10mm is perpendicular to the outside triangle
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write TURN SIGNALS between these guidelines

Sheet 15 (Aldi, pg24)

For this exercise you need your protractor and to familarise yourself with the instructions for Exercise 2 on Page 24
Fill in your name, SHEET 15: ANGLES 6 and the date
Measure 30mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 90mm horizontally along the base line and mark the point, this is the bottom left corner of the logo
From this point, draw a light construction line vertically upwards. Measure 195mm along this line. This represents the left-hand-side of the logo
From this point, draw a light construction line horizontally across the page. This represents the top of the logo. The width of the logo is not given. How do you get that? You have to complete other parts of the drawing first.
From the bottom left corner measure up 10mm and draw a horizontal line across the page, this represents the inside of the frame of logo. (When you draw a line parallel to another line it is called OFFSET. So in this case the inside line is OFFSET 10mm from the baseline)
Mark off the 10mm increments along the bottom left corner of the logo as shown in the diagram in the book.
Project these point onto the inside of the frame. Is there a better way of doing this?
What angle are the sloping lines? (the alternate angles between two lines are equal! look at page 23 of your text book)
From the bottom corner of the inside frame, draw a light construction line at 55 degrees (with the protractor). Use the sliding set-squares method (shown on page 21) to draw the other lines. (Each line is OFFSET by 10mm) How do you know where theses lines stop?
Measure and draw a construction line 10mm down from the top line of the logo. This represents the inside of the top of the logo.
Measure down and draw another horizontal construction line 10mm down from the last line. This line gives you the top of the sloping lines
The sixth sloping line gives you the top inside corner of the frame as shown in the diagram. Draw a line vertically downwards from this point.
The outside line from is OFFSET by 10mm. Measure 10mm horizontally and draw a vertical line. This gives you the right-hand side of the logo.
Measure and draw the lines that form the horizontal part of the A in Aldi as shown in the diagram. How far do they go?
You have the draw a light construction line from the seventh 10mm increment from the bottom left corner
Examine the diagram again closely and heavy in the lines to give you the Aldi logo
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write ALDI between these guidelines

Sheet 16 (Woodies, pg25)

For this exercise you need your protractor and to familarise yourself with the instructions for Exercise 3 on Page 25
Fill in your name, SHEET 16: ANGLES 7 and the date
Measure 80mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 130mm horizontally along the base line and mark the point, this is the bottom left corner of the Woodies logo
Mark off the distances along the base line as indicated in the diagram in the textbook
What angles are the lines from this point? (the alternate angles between two lines are equal! look at page 23 of your text book)
Measure 115mm vertically upwards and draw a light construction line horizontally. This represents the top of the W in the diagram
Draw two lines at 65 degrees through this bottom left corner (measure from both the left and right ends of the protractor).
Use the sliding set-squares method shown on page 21 to repeat this procedure for each point indicated along the horizontal ie: measure 65 degrees from both the left and right ends of the protractor. These should be light construction lines.
Draw heavy object lines over the construction lines to form the diagram in the textbook. Don't forget the little chimney (5mm x 15mm) at top
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write WOODIES between these guidelines

Sheet 16A (Massey Ferguson, pg25) (Optional)

For this exercise you need your protractor and to familarise yourself with the instructions for Exercise 3 on Page 25
Fill in your name, SHEET 16A: ANGLES 7A and the date
Measure 50mm vertically and draw a light construction line across the page with your T-square (This is your base line)
Measure 150mm then 80mm horizontally along the base line and mark these points, these are the two bottom points of the Massey Ferguson logo
Measure up 100mm and then 50mm. Draw horizontal construction lines through these points. These represent horizontal lines in the logo.
What angles are the lines from this point? (the alternate angles between two lines are equal!)
Draw two lines at 55 degrees through the bottom points ie: measure 65 degrees from both the left and right ends of the protractor. These should be light construction lines.
These lines so far will give you the outline shape of the logo. How do you get the smaller inside triangles?
Examine the diagram in on page 25 of the text book. Offset the central triangle by 5mm (BE CAREFUL! the 5mm is measured, perpendicular to the existing lines). How do you do this? (rotate the top set-square!)
From the bottom of the diagram, measure 10mm vertically down and draw a light horizontal guideline, measure a further 5mm and draw another light horizontal guideline.
Write MASSEY FERGUSON between these guidelines

Sheet 17 (Triangles, not in the book )

Sheet 18 (Constructing Triangles, not in the book)

Sheet 19 (Mitsubishi, pg29, Citreon, pg 30)

Sheet 20 (Adidas, pg32)

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