SOLUTIONS
GEOMETRY AND SPATIAL SENSE: CONSTRUCTION OF 2-D SHAPES
Please follow your teacher’s instructions to open The Geometer’s Sketchpad and enlarge your screen.
If you need practice using the selection
, line
and point
tools, please print and complete
Introduction to The Geometer’s Sketchpad. You can find this activity at mathfrog.ca.
1. a)
b)
c)
d)
e)
f)
g)
h)
Hold down the line tool and choose the ray tool.
Draw any angle.
Choose the selection tool.
Click on empty space.
Select the three points one at a time. Be sure that the second point is the vertex.
Click on the Measure menu and choose Angle.
Drag point A until ∠ ABC = 50°.
Clear the screen using a selection rectangle and the delete key.
2. a)
b)
c)
d)
Choose the ray tool.
Repeat question 1, parts b-f.
Drag point F until ∠ DEF = 134°.
Clear the screen using a selection rectangle and the delete key.
3. a) Hold down the ray tool and choose the line segment tool.
b) Draw a horizontal line segment.
c) Choose the selection tool.
d) Click on the Measure menu and choose Length.
e) Drag point H until GH = 8.5 cm.
f) Select the line segment tool.
g) Beginning at H, draw any line segment.
h) Choose the selection tool.
i) Click on the Measure menu and choose Length.
j) Drag point I until HI = 7.6 cm.
k) Click on empty space.
l) Select the three points in the order G, H and I.
m) Click on the Measure menu and choose Angle.
n) Drag point I until ∠ GHI = 112°. Make sure that HI = 7.6 cm.
o) Choose the line segment tool.
p) Draw a line segment from I to G.
q) Choose the selection tool.
r) Click on empty space.
Answers may vary slightly.
s) Measure GI and ∠ HGI. = 13.3cm ∠ HGI = 32°
Expectations: i) construct polygons given angle and side measurements, using a variety of tools.
4. a) Click on the File menu and choose New Sketch.
b) Repeat the processes of question 3 to construct quadrilateral ABCD with
AB = 10.6 cm, BC = 3.9 cm, ∠ ABC = 70°, CD = 7.7 cm and ∠ BCD = 137°.
c) Complete the following blanks. AD = 7.6cm ∠ ADC = 81° ∠ DAB = 72°
Answers may vary slightly.
5. a) Click on the File menu and choose New Sketch.
b) Repeat the processes of question 3 to construct
the diagram at the right.
c) Construct quadrilateral ABCD with AB = 6.0 cm,
BC = 3.5 cm, ∠ ABC = 150°, CD = 12 cm,
and ∠ BCD = 30°.
d) The length of AD is 3.4cm.
e) Select the line segment CD. Click on the
Construct menu and choose Midpoint. You have
just located point E.
f) Construct EF = 4.5 cm.
g) Construct ∠ FEC = 5°.
h) Complete FGE by constructing GE = 6 cm and
Answers may vary slightly.
∠ GEF = 90°.
i) Complete the following blanks. FG = 7.5cm
∠ FGE = 37° ∠ DEG = 85°
DID YOU KNOW?
The longest Monopoly
game ever played
lasted 1 680 hours or
70 days.
TRY THIS!
1) Use your imagination to neatly create a picture, of your choice, (as in question 5)
in your mathematics notebook.
2) Write clear instructions so that someone else will be able to recreate your
picture.
3) Give your instructions, without the picture, to a classmate.
4) Have him/her construct your picture, from your instructions, in his/her notebook.
5) Have him/her use The Geometer’s Sketchpad and your instructions to construct
your picture again.
Expectations: i) construct polygons given angle and side measurements, using a variety of tools.