Drawing Geometric Shapes

Examples, videos, and solutions to help Grade 7 students learn how to use a compass, protractor, and ruler to draw geometric shapes based on given conditions.

New York State Common Core Math Grade 7, Module 6, Lesson 6

Worksheets for Grade 7

Lesson 6 Student Outcomes

• Students use a compass, protractor, and ruler to draw geometric shapes based on given conditions.

Lesson 6 Summary

• A compass can be used to construct circles, to measure and mark off a segment of equal length to another segment, and to confirm the fact that the radius of the center of a circle to the circle itself remains constant no matter where you are on the circle.

Lesson 6 Classwork
Discussion
A compass is a tool for drawing circles. The point where the needle of the compass sits represents the center of the circle and its radius can be adjusted by widening or narrowing the two arms of the compass.
Tips to drawing circles with a thumbscrew compass:

• Adjust the compass to the intended radius length.
  
• Using one hand, place weight on the point of the compass and let the pencil-end be relatively loose.
  
• Angle the compass relative to the paper; holding the compass perpendicular to the paper will make it difficult to maneuver.

Exploratory Challenge
Use a ruler, protractor, and compass to complete the following problems.

1. Use your ruler to draw three segments of the following lengths: 4 cm, 7.2 cm, and 12.8 cm. Label each segment with its measurement.
2. Draw complementary angles so that one angle is 35°. Label each angle with its measurement. Are the angles required to be adjacent?
3. Draw vertical angles so that one angle is 135°. Label each angle formed with its measurement.
4. Draw three distinct segments of lengths 2 cm, 4 cm, and 6 cm. Use your compass to draw three circles, each with a radius of one of the drawn segments. Label each radius with its measurement.
5. Draw three adjacent angles a°, b°, and c° so that a = 25°, b = 90°, and c = 50°. Label each angle with its measurement.
6. Draw a rectangle ABCD so that AB = CD = 8 cm and BC = AD = 3 cm.
7. Draw a segment AB that is 5 cm in length. Draw a second segment that is longer than AB and label one endpoint C. Use your compass to find a point on your second segment, which will be labeled D, so that CD = AB.

8. Draw a segment AB with a length of your choice. Use your compass to construct two circles:
   i. A circle with center A, and radius AB.
   ii. A circle with center B, and radius BA.
   Describe the construction in a sentence.
   
9. Draw a horizontal segment AB, 12 cm in length.
   a. Draw a point O on AB that is 4 cm from B.
   b. Point O will be the vertex of an angle COB.
   c. Draw ray OC so that the ray is above AB and angle COB is 30°.
   d. Draw a point P on AB that is 4 cm from A.
   e. Point P will be the vertex of an angle QPO.
   f. Draw ray PQ so that the ray is above AB and angle QPO = 30°.
   
10. Draw segment AB of length 4 cm. Draw the same circle from A and from B(i.e., do not adjust your compass in between) with a radius of a length that allows the two circles to intersect in two distinct locations. Label the points where the two circles intersect C and D. Join A and C with a segment; join B and C with a segment. Join A and D with a segment; join B and D with a segment.
    What kind of triangles are triangle ABC and triangle ABD? Justify your response.
    
11. Determine all possible measurements in the following triangle and use your tools to create a copy of it.

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