Chapter 10 – Conceptual Building Blocks
CONSTRUCTIONS AND LOCI
Construction 1
Segment Congruent
To Given Segment
Start
Step 1
Step 2
Step 3
Finish
Construction 2
Angle Congruent
To Given Angle
Construction 3
Angle Bisector
Start
Start
Step 1
Step 1
Step 2
Step 2
Step 3
Step 3
Finish
Finish
Construction 4
Perpendicular Bisector
of Line Segment
Construction 5
Start
Start
Step 1
Step 1
Step 2
Finish
Step 2
Step 3
Finish
Step 2
Step 3
Finish
Perpendicular Bisector of
Line from Point on Line
Construction 6
Perpendicular Bisector
of Line from Point
Not on Line
Start
Step 1
Parallel to line through
point not on the line
Start
Construction 7
Step 1
Step 2
1
2
h
k
< 1 = < 2 Æ h || k
Postulate 11
Step 4
Step 3
Step 5
Justification
Tangent to
Point on Circle
Construction 8
Start
Step 1
Step 2
tangent
Theorem 9-2
Step 3
Step 4
Step 5
Justification
Tangent to circle from
Outside Point
Construction 9
Step 1
Step 2
Step 3
Step 4
tangent
Step 5
Justification
Circumscribe a circle
about a triangle
Step 1
Theorem 9-2
Th 9-7, Cor 2
Step 2
Construction 10
seg ⊥ bisectors Æ
circumscribed circle
Step 3
Step 4
Theorem 10 -2
Justification
Inscribing a circle
inside a triangle
Construction 11
Step 1
Step 2
Justification
Step 3
Step 4
Step 5
angle bisectors Æ
inscribed circle
Theorem 10 -1
Divide line segment
Divide
line segment
into equal
parts
into equal parts
Start
Start
Construction 12
Construction 12
Step 3
Step 1
Step 2
Step 1
Step 2
Step 4
Step 3
Step 5
Step 4
Step 5
Justification
a
Step 7
Step 6
Step 8
Step 7
Step 6
x
y
b
Step 8
a=b→x=y
Theorem 5 - 9
c
c
a
b
c
c
x
Construct x
such that
a
a
b
a c
=
b x
b
Step 1
Construction 13
c
a
b
c
a
c
a
b
a
b
Step 4
Step 3
Step 2
b
Step 5
Step 6
Justification
c
a
a
c
x
a
b
b
Step 7
x
b
c
x
Step 8
a c
=
b x
Theorem 7 - 3
a
b
x
a
Construct GEOMETRIC
MEAN x such that
b
a x
=
x
b
Construction 14
Step 1
Step 2
Step 3
x
a
Step 5
Step 4
b
Step 6
Step 7
a
b
x
x
x
a x
=
x
b
Step 8
a
a x
=
x
b
b
a
Th 9-7, Cor 2
b
Theorem 8 – 1, Cor 1
Justification
2
3
angle bisectors Æ
inscribed circle
seg ⊥ bisectors Æ
circumscribed circle
altitudes X point
1
3
Theorem 10 - 1
Theorem 10 - 2
Theorem 10 - 3
Theorem 10 - 4