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CHAPTER 1: Tools of Geometry

CHAPTER 1: Tools of Geometry. Section 1-7: Basic Constructions. Objectives. To use a compass and a straightedge to construct congruent segments and congruent angles. To use a compass and a straightedge to bisect segments and angles. Vocabulary. Construction Straightedge Compass

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CHAPTER 1: Tools of Geometry

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  1. CHAPTER 1:Tools of Geometry Section 1-7: Basic Constructions

  2. Objectives • To use a compass and a straightedge to construct congruent segments and congruent angles. • To use a compass and a straightedge to bisect segments and angles.

  3. Vocabulary • Construction • Straightedge • Compass • Perpendicular Lines • Perpendicular Bisector • Angle Bisector

  4. Construction • In a construction you use a straightedge and a compass to draw a geometric figure.

  5. Straightedge • A straightedge is a ruler with no markings on it.

  6. Compass • A compass is a geometric tool used to draw circles and parts of circles called arcs.

  7. Construction #1:Constructing Congruent Segments • Given: AB • Construct: CD so that CD is congruent to AB • Steps: • Draw a ray with endpoint C. • Open the compass to the length of AB. • With the same compass setting, put the compass on C and draw an arc that intersects the ray. Label the intersection D. • CD is congruent to AB

  8. Construction #2:Constructing Congruent Angles • Given: RA • Construct: RS so that RS is congruent to RA • Steps: • Draw a ray with endpoint S. • With the compass on point A, draw an arc that intersects the sides of RA. Label the points of intersection B and C. • With the same compass setting, put the compass point on S. Draw an arc and label its point of intersection with the ray as R. • Open the compass to the length of BC. Keeping the same compass setting, put the compass on R. Draw an arc to locate point T. • Draw ST. • RS is congruent toRA

  9. Perpendicular Lines • Perpendicular lines are two lines that intersect to form a right angle.

  10. Perpendicular Bisector • A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to a segment at its midpoint. • It bisects the segment into two congruent segments.

  11. Construction #3:Constructing the Perpendicular Bisector • Given: AB • Construct: XY so that XY is perpendicular to AB at the midpoint M of AB. • Steps: • Put the compass point on point A and draw a long arc– be sure the opening is greater than half of AB. • With the same compass setting, repeat step one, this time with the compass on point B. Label the two intersection points X and Y. • Draw XY.

  12. Angle Bisector • An angle bisector is a ray that divides an angle into two congruent coplanar angles. • The ray “bisects” the angle.

  13. Construction #4:Constructing the Angle Bisector • Given: RA • Construct: AX, the bisector of RA. • Steps: • Put the compass point on vertex A. Draw an arc that intersects both sides of the angle. Label those points B and C. • Put the compass point on C and draw an arc in the interior of the angle. • Repeat step two, this time with the compass point on B. • Label the intersection point of the two arcs X. • Draw AX.

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