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Construction Techniques: Copying Segments and Angles with Compass and Straightedge

This guide outlines essential construction techniques using only a compass and a straightedge. Learn the definitions, such as what constitutes an arc, and step-by-step instructions for copying line segments and angles. With clearly labeled diagrams and steps, students will understand how to create congruent segments and angles without measuring distances. Mastering these fundamental skills will enhance your geometric construction abilities, setting a solid foundation for more complex constructions.

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Construction Techniques: Copying Segments and Angles with Compass and Straightedge

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Presentation Transcript

  1. Basic Constructions Copy a segment Copy an angle

  2. What is a Construction? • Uses TWO instruments only • Compass • Straightedge • Since a compass measures the radius of a circle, and radii of a circle are congruent, then we can use it to construct congruent segments. • A straightedge is used to connect two points. A ruler may not be used to measure distances in constructions.

  3. What is a Construction? • Definition: • An arc is any part of a circle. • When we draw using a compass we will be drawing arcs. We rarely need to complete the entire circle. The radii will still be congruent even if a complete circle is not present.

  4. Given , construct a segment congruent to on line l. A B Put compass point here Put compass point here l C D Construction #1: Copy a Segment Step 1: Use the straightedge to draw a line and label it l Step 2: Choose any point on l and label it C. Step 3: Set the compass at A and make an arc at B. Step 4: Using the same opening, set your compass at C and make an identical arc so that it intersects line l. Label this point D.

  5. C Put compass point here Put compass point here Put compass point here l F Construction #2: Copy an Angle Step 1: You need to start with a line l and a point F which corresponds to C. E Step 2: Opening your compass to any comfortable distance, set the compass at C and make an arc that intersects both sides of the angle. Label these points E and D. D Step 3: Using the same opening, set the compass at F and make an identical arc which intersects the line l. Label this point G. Step 4: On the original angle, set the compass at D and make an arc that intersects the other side of the angle at E. G

  6. E Step 6: Draw C D Put compass point here G F Construction #2: Copy an Angle Step 5: Using the same opening, set your compass at G and make an identical arc so that it intersects the arc from step 3. Label this point H. H

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