Download Section 1-7: Basic Constructions

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
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Construction
Straightedge
Compass
Perpendicular Lines
Perpendicular Bisector
Angle Bisector
Construction
 In a construction you use a straightedge and a
compass to draw a geometric figure.
Straightedge
 A straightedge is a ruler with no markings on
it.
Compass
 A compass is a geometric tool used to draw
circles and parts of circles called arcs.
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
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 to RA
Perpendicular Lines
 Perpendicular lines are two lines that intersect
to form a right angle.
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.
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.
Angle Bisector
 An angle bisector is a ray that divides an angle
into two congruent coplanar angles.
 The ray “bisects” the angle.
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.