Download Slide 1 - NEHSMath

Section 1-5: Constructions
SPI 32A: Identify properties of plane figures
TPI 42A: Construct bisectors of angles and line segments
Objective:
• Use a compass and straight edge to construct and
bisect congruent segments and angles
Perpendicular Lines 
Two lines that intersect to form right angles.
Perpendicular Bisector
A line, segment, or ray that is perpendicular
to the segment at its midpoint, thereby
bisecting the segment into two congruent
segments.
2 congruent segments
midpoint
Angle Bisector
Ray that divides an angle into two congruent coplanar
angles.
• Its endpoint is the angle vertex
• Say… Ray or Segment bisects the angle
Tools used for Geometric Constructions
Straight Edge
Ruler with no markings
Compass
Tool used to draw circles
or arcs
Next, you will learn to construct:
1. Congruent Segments
2. Congruent Angles
3. Perpendicular Bisectors
4. Angle Bisectors
Construct Congruent Segments with Straight Edge and Compass
Construct a segment congruent to a given segment.
Given: AB
Construct: CD so that CD  AB
Step 1: Draw a ray with endpoint C
A
C
Step 2: Open a compass to the length AB
Step 3: With the same compass setting, put
the compass point on point C. Draw
an arc that intersects the ray. Label
the point of intersection D.
CD  AB
B
Construct Congruent Angles using Straight Edge and Compass
Construct an angle congruent to a given angle.
Given:  A
Construct: S so that S  A
Step 1: Draw a ray with endpoint S.
A
S
Step 2: With the compass point on point A,
draw an arc that intersects the sides of A.
Label the points of intersection B and C.
Step 3: With the same compass setting, put
the compass point on point S. Draw an arc
and label its point of intersection with the ray as R.
Step 4: Open the compass to length BC. Keeping
the same compass setting, put the compass point
on R. Draw an arc to locate point T.
Step 5: Draw ST.
Construct Perpendicular Bisector
Construct the perpendicular bisector of a segment.
Given: AB
Construct: XY so that XY  AB at the midpoint
M of AB
Step 1: Put the compass of point A and draw a
long arc as shown. Be sure the opening is
greater than ½ AB.
Step 2: With the same compass setting, put the
compass point on point B and draw another
long arc. Labe the points where the two arcs
intersect as X and Y.
Step 3: Draw XY. The point of intersection of AB
and XY is M, the midpoint of AB.
XY  AB at the midpoint of AB, so XY is the
Perpendicular bisector of AB.
A
B
Construct Angle Bisector
Construct the bisector of an angle
Given: A
Construct: AX, the bisector of A
Step 1: Put the compass of vertex A. Draw an
arc that intersects the sides of A. Label the
points of intersection B and C.
Step 2: Put the compass point on point C and
draw an arc. With the same compass setting,
draw an arc using point B. Be sure the arcs
intersect. Label the intersection as X.
Step 3: Draw AX.
AX is the bisector of CAB.
Construction and Vocabulary Activity
1. Use your compass to draw a circle.
2. Locate three points A, B, and C on the circle.
3. Construct perpendicular bisectors of AB and BC.
4. Label the intersection of the two perpendicular bisectors
as point O.
5. Make a conjecture about point O.