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 PossibleClasswork1. 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 mb. 8 yd, 5 yd, 13 ydc. 7 in, 15 in, 23 ind. 24 ft, 35 ft, 58 fte. 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 inb. 7 m, 32 mc. 8 in, 12 ind. 12 cm, 15 cme. 43 yd, 57 yd

Homework4. 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 mb. 13 yd, 9 yd, 23 ydc. 13 in, 23 in, 36 ind. 5 ft, 23 ft, 29 fte. 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 inb. 17 m, 26 mc. 12 in, 25 ind. 9 cm, 18 cme. 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 inb. 15 m, 27 m, 41 mc. 9 yd, 9 yd, 17 ydd. 4 ft, 9 ft, 13 ft

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Geometric Constructions: The BasicsClassworkCircle Constructions8. Draw a circle that has a radius of 5 cm using

a ruler & a compass.

9. Draw a circle that has a radius of 4.3 cm using a ruler & a compass.

10. Draw a circle that has a diameter of 7 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 Constructions12. 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 Triangles14. 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 Conditions16. 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 ∆≝¿ 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

HomeworkCircle Constructions20. Draw a circle that has a radius of 3 cm using

a ruler & a compass.

21. Draw a circle that has a radius of 2.4 cm using a ruler & a compass.

22. Draw a circle that has a diameter of 5 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 Constructions24. 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 Triangles26. 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 Conditions28. 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. Yes; 4 + 12 > 15 16 > 15 b. No; 5 + 8 > 13 13≯� 13c. No; 7 + 15 > 23 22≯� 23d. Yes; 24 + 35 > 58 59 > 58e. No; 18 + 27 > 46 45≯� 46

2.a. Yes; 45 + 57 + 78 = 180b. No; 90 + 54 + 26 = 170 ≠ 180c. No; 104 + 90 + 34 = 228 ≠ 180d. No; 55 + 91 + 105 = 251 ≠ 180e. Yes; 56 + 45 + 79 = 180

3.a. 18 in < Third Side < 28 inb. 25 m < Third Side < 39 mc. 4 in < Third Side < 20 ind. 3 cm < Third Side < 27 cme. 14 yd < Third Side < 100 yd

4.a. Yes; 7 + 11 > 17 18 > 17b. No; 9 + 13 > 23 22≯� 23c. No; 13 + 23 > 36 36≯� 36d. No; 5 + 23 > 29 28≯� 29e. Yes; 27 + 35 > 46 62 > 46

5.a. No; 52 + 37 + 95 = 184 ≠ 180b. Yes; 107 + 39 + 34 = 180c. No; 112 + 90 + 68 = 270 ≠ 180d. No; 52 + 94 + 108 = 254 ≠ 180e. Yes; 48 + 53 + 79 = 180

6.a. 29 in < Third Side < 45 inb. 9 m < Third Side < 43 mc. 13 in < Third Side < 37 ind. 9 cm < Third Side < 27 cme. 17 yd < Third Side < 181 yd

7. D8. Check Constructions; diagram should

resemble the figure below.

9. Check Constructions; diagram should resemble the figure below.

10. Check Constructions; diagram should resemble the figure below.

11. Check Constructions; diagram should resemble the figure below.

12. Check Constructions; diagram should resemble the figure below.

13. Check Constructions; diagram should resemble the figures below.

OR

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14. Check Constructions; diagram should resemble the figure below.

15. Check Constructions; diagram should resemble the figure below.

16. Check Constructions; diagram should resemble the figure below.

17. Check Constructions; diagram should resemble the figure below.

18. Check Constructions; diagram should resemble the figure below.

19. Check Constructions; diagram should resemble the figure below.

20. Check Constructions; diagram should resemble the figure below.

21. Check Constructions; diagram should resemble the figure below.

22. Check Constructions; diagram should resemble the figure below.

23. Check Constructions; diagram should resemble the figure below.

24. Check Constructions; diagram should resemble the figure below.

25. Check Constructions; diagram should resemble the figures below.

OR

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26. Check Constructions; diagram should resemble the figure below.

27. Check Constructions; diagram should resemble the figure below.

28. Check Constructions; diagram should resemble the figure below.

29. Check Constructions; diagram should resemble the figure below.

30. Check Constructions; diagram should resemble the figure below.

31. Check Constructions; diagram should resemble the figure below.

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