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Basic Constructions

Basic Constructions. Copy a segment Copy an angle. 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.

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Basic Constructions

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  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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