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A. Prentice-Hall 9.7 introduction
1. We will be talking about constructions today, which is truly something hand’s on!
a. This means you make geometric segments or angles using only a compass and a
straight edge, but you DON’T use the straight edge as a ruler
1) Note: the above limits were noted in 300 BC by Euclid in Elements
b. The compass allows you to compare two lengths even though they aren’t measured in
units
c. A compass lets you draw circles or parts of circles (i.e., arcs)
B. Construct a segment congruent to AB
A
1. With the straight edge, draw a ray with endpoint C
B
C
2. Open the compass to the length of AB
3. With the same compass setting, put the compass tip on C.
a. Draw an arc that intersects the ray and label that intersection as D
b. AB  CD
C
C. Construct an angle congruent to E
D
E
1. With the straight edge, draw a ray with endpoint Q
Q
F
2. With the compass point at E, draw an arc that intersects the sides of E
E
3. With the same compass setting, put the compass tip on Q
G.
a. Draw an arc that intersects the ray and label that intersection as P
Q
P
4. Open the compass to the length of FG and put the compass tip at P
R
a. Draw an arc to determine the point R & draw
b. Q  E
Q
P
D. Bisectors
1. A bisector divides a segment or an angle in half (so have two congruent segments/angles)
a. A segment bisector is a line/segment/ray that divides a segment into two congruent
segments
b. A perpendicular bisector is a line/segment/ray that is perpendicular to the segment it
bisects
c. An angle bisector is a ray that divides an angle into two congruent angles
Prentice Hall 9.7 Lecture notes (Constructions) - 1
E. Construct the perpendicular bisector of PQ
P
Q
1. Open the compass to more than half of the length of PQ
a. Put the compass tip at P
P
Q
b. Draw an arc above and below PQ
S
2. Repeat the above but do it with point Q
P
T
Q
3. Label the points of intersection S and T
a. Draw
b.
P
S
Q
bisects
F. Construct the bisector of  A
T
A
1. Put the compass tip at A
2. Draw an arc that intersects the sides of  A
A
a. Label the points of intersection as B and C
C
B
3. Put the compass tip at B
a. Draw an arc
b. With the same compass setting, repeat with the compass tip at C
1) Make sure the arcs intersect!
A
C
B
D
4. Label the intersection of the arcs as D
a. Draw
b.
bisects ÐBAC
G. Construct an equilateral triangle (adapted from http://www.wikihow.com/Draw-an-Equilateral-Triangle)
1. Draw a line segment with the straight edge
2. Put the point of your compass at one end of the segment and the pencil point at the other
a. Without moving the point of the compass and without changing how
wide it is set, swing the compass in approximately a ¼ circle
(up & away from the line segment).
3. Without changing how wide the compass is spread, move the compass point to the other end.
a. Swing the compass so that the arc you are creating crosses the arc you drew
4. Mark the place where the two arcs cross. This is the apex of your triangle.
5. Using a ruler, draw line segments that connect the spot
where the arcs cross to each end of the original line segment.
Prentice Hall 9.7 Lecture notes (Constructions) - 2