Drawing Geometric Figures: Chapter Questions
1.
Can we determine if three side lengths would create a triangle?
2.
How do we construct a circle with a ruler and compass?
3.
How do we construct a triangle with a compass, ruler, and/or protractor?
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Drawing Geometric Figures: Chapter Problems
Determining if a Triangle is Possible
Classwork
1. Determine if triangles can be formed with the following side lengths. Explain your answer w/ a
drawing, math expression, and/or words:
a. 4 m, 12 m, 15 m
b. 8 yd, 5 yd, 13 yd
c. 7 in, 15 in, 23 in
d. 24 ft, 35 ft, 58 ft
e. 18 cm, 27 cm, 46 cm
2. Which of the following sets of angles could form a triangle? Explain your answer w/ a drawing, math
expression, and/or words.
a. 45°, 57°, 78°
b. 90°, 54°, 26°
c. 104°, 90°, 34°
d. 55°, 91°, 105°
e. 56°, 45°, 79°
3. Predict the length of the third side of a triangle whose known sides are lengths:
a. 5 in, 23 in
b. 7 m, 32 m
c. 8 in, 12 in
d. 12 cm, 15 cm
e. 43 yd, 57 yd
Homework
4. Determine if triangles can be formed with the following side lengths. Explain your answer w/ a
drawing and/or words:
a. 7 m, 11 m, 17 m
b. 13 yd, 9 yd, 23 yd
c. 13 in, 23 in, 36 in
d. 5 ft, 23 ft, 29 ft
e. 27 cm, 35 cm, 46 cm
5. Which of the following sets of angles could form a triangle? Explain your answer w/ a drawing, math
expression, and/or words:
a. 52°, 37°, 95°
b. 107°, 39°, 34°
c. 112°, 90°, 68°
d. 52°, 94°, 108°
e. 48°, 53°, 79°
6. Predict the length of the third side of a triangle whose known sides are lengths:
a. 8 in, 37 in
b. 17 m, 26 m
c. 12 in, 25 in
d. 9 cm, 18 cm
e. 82 yd, 99 yd
7. Multiple Choice: Determine which set of sides cannot be used to form a triangle.
a. 8 in, 9 in, 15 in
b. 15 m, 27 m, 41 m
c. 9 yd, 9 yd, 17 yd
d. 4 ft, 9 ft, 13 ft
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Geometric Constructions: The Basics
Classwork
Circle Constructions
8. Draw a circle that has a radius of 5 cm using
a ruler & a compass.
10. Draw a circle that has a diameter of 7 cm
using a ruler & a compass.
9. Draw a circle that has a radius of 4.3 cm
using a ruler & a compass.
11. Draw a circle that has a diameter of 4.8 cm
using a ruler & a compass.
Isosceles Triangle Constructions
12. Use a ruler & a compass to draw an isosceles triangle w/ the following conditions:
 At least one side measures 4 cm.
 At least one side measures 1.5 cm.
13. Use a ruler & a compass to draw an isosceles triangle w/ the following conditions:
 At least one side measures 7 cm.
 At least one side measures 5 cm.
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Equilateral Triangles
14. Use a ruler & a protractor to draw an equilateral triangle that has a side length of 4 cm.
15. Use a ruler & a protractor to draw an equilateral triangle that has a side length of 3.6 cm.
Constructing a Triangle with Given Conditions
16. Use a ruler & a protractor to draw ∆𝐴𝐵𝐶 that satisfies the following conditions:
 𝑚∠𝐴 = 90°
 𝑚∠𝐵 = 25°
 𝐴𝐵 = 3 cm
17. Use a ruler & a protractor to draw ∆𝐷𝐸𝐹 that satisfies the following conditions:
 𝑚∠𝐷 = 110°
 𝑚∠𝐹 = 30°
 𝐷𝐹 = 4 cm
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18. Use a ruler & a protractor to draw ∆𝐺𝐻𝐼 that satisfies the following conditions:
 𝑚∠𝐺 = 80°
 𝐺𝐻 = 4 cm
 𝐺𝐼 = 3.5 cm
19. Use a ruler & a protractor to draw ∆𝐽𝐾𝐿 that satisfies the following conditions:
 𝑚∠𝐾 = 120°
 𝐽𝐾 = 2 cm
 𝐾𝐿 = 2.5 cm
Homework
Circle Constructions
20. Draw a circle that has a radius of 3 cm using
a ruler & a compass.
22. Draw a circle that has a diameter of 5 cm
using a ruler & a compass.
21. Draw a circle that has a radius of 2.4 cm
using a ruler & a compass.
23. Draw a circle that has a diameter of 6.4 cm
using a ruler & a compass.
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Isosceles Triangle Constructions
24. Use a ruler & a compass to draw an isosceles triangle w/ the following conditions:
 At least one of the sides measures 2.5 cm.
 At least one of the sides measures 1 cm.
25. Use a ruler & a compass to draw an isosceles triangle w/ the following conditions:
 At least one of the sides measures 6.5 cm.
 At least one of the sides measures 4 cm.
Equilateral Triangles
26. Use a ruler & a protractor to draw an equilateral triangle that has a side length of 3.5 cm.
27. Use a ruler & a protractor to draw an equilateral triangle that has a side length of 4.7 cm.
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Constructing a Triangle with Given Conditions
28. Use a ruler & a protractor to draw ∆𝑀𝑁𝑂 that satisfies the following conditions:
 𝑚∠𝑀 = 90°
 𝑚∠𝑁 = 60°
 𝑀𝑁 = 2.5 cm
29. Use a ruler & a protractor to draw ∆𝑃𝑄𝑅 that satisfies the following conditions:
 𝑚∠𝑃 = 75°
 𝑚∠𝑅 = 50°
 𝑃𝑅 = 3 cm
30. Use a ruler & a protractor to draw ∆𝑆𝑇𝑈 that satisfies the following conditions:
 𝑚∠𝑆 = 105°
 𝑆𝑈 = 1.5 cm
 𝑆𝑇 = 2.3 cm
31. Use a ruler & a protractor to draw ∆𝑉𝑊𝑋 that satisfies the following conditions:
 𝑚∠𝑊 = 90°
 𝑉𝑊 = 5 cm
 𝑊𝑋 = 12 cm
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Answer Key
1.
a.
b.
c.
d.
e.
Yes; 4 + 12 > 15  16 > 15
No; 5 + 8 > 13  13 ≯ 13
No; 7 + 15 > 23  22 ≯ 23
Yes; 24 + 35 > 58  59 > 58
No; 18 + 27 > 46  45 ≯ 46
a.
b.
c.
d.
e.
Yes; 45 + 57 + 78 = 180
No; 90 + 54 + 26 = 170 ≠ 180
No; 104 + 90 + 34 = 228 ≠ 180
No; 55 + 91 + 105 = 251 ≠ 180
Yes; 56 + 45 + 79 = 180
a.
b.
c.
d.
e.
18 in < Third Side < 28 in
25 m < Third Side < 39 m
4 in < Third Side < 20 in
3 cm < Third Side < 27 cm
14 yd < Third Side < 100 yd
a.
b.
c.
d.
e.
Yes; 7 + 11 > 17  18 > 17
No; 9 + 13 > 23  22 ≯ 23
No; 13 + 23 > 36  36 ≯ 36
No; 5 + 23 > 29  28 ≯ 29
Yes; 27 + 35 > 46  62 > 46
a.
b.
c.
d.
e.
No; 52 + 37 + 95 = 184 ≠ 180
Yes; 107 + 39 + 34 = 180
No; 112 + 90 + 68 = 270 ≠ 180
No; 52 + 94 + 108 = 254 ≠ 180
Yes; 48 + 53 + 79 = 180
a.
b.
c.
d.
e.
29 in < Third Side < 45 in
9 m < Third Side < 43 m
13 in < Third Side < 37 in
9 cm < Third Side < 27 cm
17 yd < Third Side < 181 yd
9. Check Constructions; diagram should
resemble the figure below.
4.3 cm
2.
10. Check Constructions; diagram should
resemble the figure below.
3.
7 cm
4.
11. Check Constructions; diagram should
resemble the figure below.
4.8 cm
5.
12. Check Constructions; diagram should
resemble the figure below.
4 cm
6.
1.5 cm
4 cm
13. Check Constructions; diagram should
resemble the figures below.
7. D
8. Check Constructions; diagram should
resemble the figure below.
7 cm
5 cm
7 cm
OR
5 cm
5 cm
7 cm
5 cm
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14. Check Constructions; diagram should
resemble the figure below.
4 cm
20. Check Constructions; diagram should
resemble the figure below.
3 cm
4 cm
21. Check Constructions; diagram should
resemble the figure below.
4 cm
15. Check Constructions; diagram should
resemble the figure below.
2.4 cm
22. Check Constructions; diagram should
resemble the figure below.
3.6 cm
3.6 cm
3.6 cm
5 cm
16. Check Constructions; diagram should
resemble the figure below.
C
A
25°
3 cm
23. Check Constructions; diagram should
resemble the figure below.
B
6.4 cm
17. Check Constructions; diagram should
resemble the figure below.
24. Check Constructions; diagram should
resemble the figure below.
E
D
110° 30°
4 cm
2.5 cm
F
1 cm
2.5 cm
18. Check Constructions; diagram should
resemble the figure below.
25. Check Constructions; diagram should
resemble the figures below.
I
3.5 cm
G
80°
4 cm
H
6.5 cm
19. Check Constructions; diagram should
resemble the figure below.
L
2.5 cm
4 cm
6.5 cm
OR
6.5 cm
120°
4 cm
K 2 cm J
4 cm
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26. Check Constructions; diagram should
resemble the figure below.
29. Check Constructions; diagram should
resemble the figure below.
Q
3.5 cm
3.5 cm
P
3.5 cm
31. Check Constructions; diagram should
resemble the figure below.
4.7 cm
V
28. Check Constructions; diagram should
resemble the figure below.
5 cm
N
M
R
U
1.5 cm 105°
S 2.3 cm T
4.7 cm
2.5 cm
50°
3 cm
30. Check Constructions; diagram should
resemble the figure below.
27. Check Constructions; diagram should
resemble the figure below.
4.7 cm
75°
W
60°
12 cm
X
O
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