SOLUTIONS
GEOMETRY AND SPATIAL SENSE: CONSTRUCTING AND MEASURING ANGLES AND
TRIANGLES
1.
In your mathematics notebook, use your ruler and protractor to draw:
a) ∠ ABC = 50°
b) ∠ DEF = 80°
c) ∠ GHI = 35°
d) ∠ JKL = 72°
e) ∠ MNO = 90°
f) ∠ PQR = 140°
g) ∠ STU = 117°
h) ∠ VWX = 154°
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.
2.
a) Hold down the line tool and choose the ray tool.
b) Draw any angle.
3.
a) Choose the selection tool.
b) Click on empty space.
4.
a) Select the three points one at a time. Be sure that the second
point is the vertex.
b) Click on the Measure menu. Choose Angle.
c) Drag point A until ∠ ABC = 50°.
You have just completed question 1(a) above.
d) Clear the screen using a selection rectangle and the delete key.
5.
Use The Geometer’s Sketchpad to redo question 1, parts b-h, above.
For each angle, you will need to repeat the processes of
questions 2, 3 and 4.
6.
In your mathematics notebook, use your protractor
and ruler to construct:
a) ABC with AB = 6 cm, ∠ ABC = 70°, and BC = 8 cm.
The size of ∠ BAC is 67°.
Answers may vary slightly.
b) DEF with DE = 6.8 cm, ∠ DEF = 90°, EF = 8.8 cm.
The length of DF is 11.2cm.
c) GHI with GH = 5.5 cm, ∠ GHI = 120°, and HI = 5.5 cm.
The size of ∠ GIH is 30°.
d) JKL with JK = 3.2 cm, ∠ JKL = 32°, and KL = 6.3 cm.
The size of ∠ JLK is 26°.
Expectations: i) measure and construct angles up to 180°; ii) construct triangles, using a variety of tools, given angle and side measurements.
7. Click on the File menu. Choose New Sketch.
8. a) Hold down the ray tool and choose the line segment tool.
b) Draw a horizontal line.
c) Choose the selection tool.
d) Click on the Measure menu and choose Length.
e) Drag point B so that AB = 6 cm.
9. a) Select the line segment tool.
b) Beginning at B, draw any line segment.
c) Choose the selection tool.
d) Click on the Measure menu and choose Length.
e) Drag point C so that BC = 8 cm.
f) Click on empty space.
10. a) Select the three points in the order A, B and C.
b) Click on the Measure menu and choose Angle.
c) Drag point C until ∠ ABC = 70°. Make sure that BC = 8 cm.
d) Choose the line segment tool.
e) Draw a line segment from C to A.
f) Choose the selection tool.
g) Click on empty space.
h) Measure ∠ BAC. ∠ BAC = 66° Answers may vary slightly.
You have just completed question 6 (a).
i) Clear the screen using a selection rectangle and the delete key.
DID YOU KNOW?
An apple, onion, and
potato all have the
same taste.
The
differences in flavor
are caused by their
smell. To prove this,
pinch your nose and
take a bite from each.
All will taste sweet.
11. Use The Geometer’s Sketchpad to redo question 6, parts b-d. You will need to repeat the
process of questions 8, 9 and 10 for each triangle. Note: The numbers and letters will be
different. Don’t forget to complete the blanks below.
The length of DF is 11.1cm.
The size of ∠ GIH is 30°.
Answers might vary slightly.
The size of ∠ JLK is 25°.
TRY THIS!
a) A pentagram is a 5-pointed star. The angle at each of the five “points”
of a regular pentagram (star) is 36°. Use The Geometer’s Sketchpad
to construct a regular pentagram. Make sure the distance between any
two “joined points” is 10 cm.
b) Now use The Geometer’s Sketchpad and your artistic talents to create a design of
your choice.
Expectations: i) measure and construct angles up to 180°; ii) construct triangles, using a variety of tools, given angle and side measurements.