Chapter Tests
and Problems
Chapter 7 Drafting Geometry
Test
INSTRUCTIONS
Answer the questions with short, complete statements or drawings as needed.
QUESTIONS
1. What is known to be true about the opposite angles created
by intersecting lines?
2. Define parallel lines.
3. Define perpendicular.
4. How many degrees are there in a circle?
5. How are angles sized?
6. Name four basic types of angles.
7. Define triangle.
8. Show how an angle is named.
9. Name and show an example of three types of triangles.
10. Show two methods of naming triangles.
11. Name three types of quadrilaterals.
19. Compare the characteristics of a square and rectangle.
20. Give the number of sides found on each of the following
regular polygons: triangle, square, pentagon, hexagon, and
octagon.
Chapter 7 Drafting Geometry
Problems
INSTRUCTIONS
1. Problems 7.21 through 7.44 use an appropriately sized
ASME sheet with sheet blocks and complete the title block
information, unless otherwise specified by your instructor.
2. Use construction lines for all preliminary work on a construction layer. Use visible object lines for the completed problem.
Leave the construction layer on when you complete the problems, unless otherwise specified by your instructor. This
helps your instructor observe your drafting technique.
3. Geometric construction problems are presented as written
instructions, drawings, or a combination of both. If the
problems are presented as drawings without dimensions,
then transfer the drawing from the text to your drawing
sheet using 1:1 scales. Draw dimensioned problems full
scale (1:1) unless otherwise specified. Draw all object lines,
hidden lines, and centerlines. Do not draw dimensions.
12. What name is given to the distance from the center to the
circumference of a circle?
Part 1: Problems 7.1 Through 7.20
13. What is the name of the distance that goes across a circle
through its center?
Problem 7.1 Draw two tangent circles with their centers on a
horizontal line. Circle 1 has a 64-mm diameter, and circle 2 has a
50-mm diameter.
Problem 7.2 Make a perpendicular bisector of a horizontal
line that is 79 mm long.
Problem 7.3 Make an angle 488 with one side vertical. Bisect
the angle.
Problem 7.4 Divide a 96-mm line into seven equal spaces.
Problem 7.5 Draw two parallel horizontal lines each 50 mm
long with one 44 mm above the other. Divide the space between
the lines into eight equal spaces.
14. What is a circle called that touches the flats of a polygon?
15. What is a circle called that touches the corners of a
polygon?
16. Sketch and label an example of concentric and eccentric
circles.
17. Sketch an example of a line tangent to a circle and two
circles tangent to each other.
18. Identify the angle formed by a perpendicular bisector.
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 1
03/02/16 10:24 am
Problem 7.6 Transfer triangle abc to a new position with
side c 45° from horizontal.
a
b
Problem 7.17 Draw two circles with 25-mm diameters and
38 mm between centers on horizontal. On the upper side between the two circles, draw an inside radius of 44 mm. On the
lower side, draw an outside radius of 76 mm.
Problem 7.18 Draw an S curve with equal radii between
points A and B given below:
c
B
Problem 7.7 Make a right triangle with one side 35 mm long
and the other side 50 mm long.
A
Problem 7.8 Make a right triangle with the hypotenuse
75 mm long and one side 50 mm long.
Problem 7.9 Make an equilateral triangle with 65-mm sides.
Problem 7.10 Make a square with a distance of 50 mm
across the flats.
Problem 7.11 Draw a hexagon with a distance of 2.5 in.
across the flats.
Problem 7.12 Draw a hexagon with a distance of 2.5 in.
across the corners.
Problem 7.13 Draw an octagon with a distance of 2.5 in.
across the flats.
Problem 7.14 Draw a rectangle 50 mm 3 75 mm with
12-mm radius tangent corners.
Problem 7.15 Draw two separate angles, one a 308 acute
angle and the other a 1208 obtuse angle. Then draw a .5-in. radius
arc tangent to the sides of each angle.
Problem 7.16 Given the following incomplete part, draw an
inside arc with a 2.5-in. radius tangent to ØA and line B.
Problem 7.19 Draw two lines, one on each side of the ogee
curve drawn in Problem 7.18 and .5 in. away.
Problem 7.20 Make an ellipse with a 38-mm minor diameter and a 50-mm major diameter.
Part 2: Problems 7.21 Through 7.44
The following geometric construction problems are presented as
dimensioned drawings or engineering problems. Draw dimensioned problems full scale (1:1) on an appropriately sized sheet
with border and title block, unless otherwise specified by your
instructor. Draw all object, hidden, and centerlines. Do not draw
dimensions. Properly complete the information in the title block.
Problem 7.21 Circles, corner arcs, and tangencies (in.)
Part Name: Plate Spacer
Material: .250 thick aluminum
6.25
A
4.25
8.88
6.88
B
R1.00
4X Ø1.062
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 2
03/02/16 10:24 am
Problem 7.22 Circles (in.)
Problem 7.25 Circle, arc, and tangencies (in.)
Part Name: Flange
Part Name: Bogie Lock
Material: .50 thick cast iron (CI)
Material: .25-in. thick mild steel (MS)
R2
Ø1 25/32
6
4 3/4
Problem 7.23 Circle, arcs, and tangencies (in.)
9 1/2
Part Name: Connector
Material: .25-in. thick steel
Problem 7.26 Arcs and tangencies (in.)
Ø 2.76
2.77
Part Name: Plate
R5
Material: .125-in. thick aluminum
4X R5 3/4
8
3
R3
29 5/8
4X R3 3/4
13 1/2
2
Problem 7.24 Arc tangencies (metric)
Part Name: Plate
Material: 10-mm thick HC-112
Used as a spacer to separate electronic components in a computer chassis.
560
R22
R60
20
6
(17 1/2)
REFERENCE
DIMENSION SYMBOL
ARCS TANGENT
430
302
285
60
140
650
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 3
03/02/16 10:24 am
Problem 7.27 Arcs and tangencies (in.)
Part Name: Flat Spring
Material: 26 gauge X .50 SAE 1085
2X R.844
3.199
2.754
1.195
2.988
2X R.844
8.701
Problem 7.28 Arcs, centerlines, and hidden lines (in.)
Problem 7.29 Circles, arcs, and tangencies (in.)
Part Name: Tube
Part Name: Gasket
Material: Copper
Material: .062-in. thick Neoprene
Outside Diameter: .75
Wall Thickness: .016
2X Ø1 3/16
12 1/2
11 3/8
9 1/2
4X R1 1/4
2
7.50
45 8
14
Ø.781
2
7 5/8
2 7/8
7
2.875
R 1.50
R .50
7 5/8
3 3/16
2 3/4
90 8
1
13 3/4
3X Ø1 1/16
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 4
03/02/16 10:24 am
Problem 7.30 Circle, arc, and tangencies (metric)
Problem 7.33 Arcs and tangencies (in.)
Part Name: Coupler
Part Name: Gusset
Material: SAE 1040
Material: .250 thick aluminum
Ø 70
33
Ø 50
Courtesy TEMCO
13
10.593
4X R.281
13
1.562
5.937
133
4.750
6.687
6.968
10.812
182
2X .562
R7.062
Problem 7.31 Circles, arcs, and tangencies (in.)
Part Name: Hanger
Material: Mild steel
6.231
2.30
2X Ø .58
Problem 7.34 Arcs, circles, and tangencies (in.)
R.80
Part Name: Pivot Arm
Material: Aluminum
2.12
Ø2.750
1.250
2X R
Ø1.000
Ø1.125
Ø2.00
Ø2.13
Problem 7.32 Circles, arcs, and tangencies (in.)
Ø4.25
Part Name: Bracket
3.000
Material: Aluminum
3.500
9.000
R1.30
Ø1.25
2X Ø.75
R.80
2.10
4.20
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 5
03/02/16 10:24 am
Problem 7.35 Arcs and angles (metric)
Problem 7.37 Circles, arcs, and tangencies (metric)
Part Name: Gasket
Material: .06-in. thick cork
Part Name: Support Brace
Material: .125-in. thick copper
28°
50
38°
R3
R10
35
Ø25.5
R15
6X Ø7
458
24
458
158
14
17
Ø71.5
Ø57
2X R7
6X R7.5
Ø68
8
Ø40
5
R10
R14
44
38°
42.5
28°
60
65
Problem 7.38 Multiviews (two views), circles, arcs, and
tangencies (in.)
Part Name: Bracket
Material: Cast iron
Problem 7.36 Arcs, circles, and tangencies (in.)
Part Name: Gasket
Material: .0625-in. thick bronze
.625
DRILL END ANGLE 120 8
Ø.50
1.06
1.75
2X R.50
4X Ø.50
21
R.63
DEPTH
SYMBOL
2X Ø.38
1.22
1.50
R.25
.43
R.50
R.50
1.38
.100
Ø.35 THRU
R.46
.200
1.54
R.75
Problem 7.39 Ogee curve and arcs (in.)
.87
R.75
R.75
1.00
1.88
2.25
.50
Part Name: Wrench
Material: .25-in. thick cast iron
Fillets and rounds: R.125
.62
4.12
R3.00
2X R.55
.375
.63
.65
3.24
2X R1.18
.76
.64
.375
R2.25
2X R.60
.58
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 6
03/02/16 10:24 am
Problem 7.40 Ogee curve, hexagon, and arcs (in.)
Problem 7.42 Multiview and hexagon (in.)
Part Name: Wrench
Part Name: Sleeve
Material: .25-in. thick cast iron
Material: Bronze
Fillets and rounds R.125
Draw only the view with the hexagon and circles.
Note: This engineer’s sketch shows dimensions to hidden features, which is not a standard practice.
2.375
2X 608
R.31
.20
.20
R 1. 4 0
R 1. 4 0
1. 3 13
.20
Ø. 6 2 5
.35
Problem 7.43 Hexagons and pentagons (in.)
Problem 7.41 Arc tangencies (in.)
Part Name: Gasket
Part Name: Hammer Head
Material: .06-in. thick brass
Material: Cast iron
Establish unknown dimensions to your own specifications.
R1.600
R.300
R.400
2X R
.175
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 7
03/02/16 10:24 am
Problem 7.44 Design problem
Math Problems
Part Name: Sailboat
Design the sailboat to your own specifications using the techniques discussed in this chapter.
Part 3: Problems 7.45 Through 7.50
For Problems 7.45 through 7.50, find the interior angles of these
types of regular polygons:
PROBLEM 7.45 Octagon.
PROBLEM 7.46 Equilateral triangle.
PROBLEM 7.47 Pentagon (5 sides).
PROBLEM 7.48 Decagon (10 sides).
PROBLEM 7.49 Square.
PROBLEM 7.50 How many sides does a regular polygon have
if its interior angle is 1408?
Copyright © 2017 Cengage Learning®. All Rights Reserved. May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part.
59728_ch07_EOC_ptg01.indd 8
03/02/16 10:24 am