Chapter 12 Homework Worksheet Packet: Constructions
 Please write on these worksheets
 Complete using only a compass and a straightedge. I need to see “arc marks” where
you used your compass.
 Detach each worksheet from this packet as you complete each one
 Staple completed work to the textbook portion of your homework
HW #23: (#1-8) Congruent segments
Congruent Segments: For #1 – 2, construct a segment congruent to the given segment.
1.)
_______________
2.)
______________________________
Special Right Triangles: For #3 - 5, solve for x and y.
3.)
4.)
5.)
45
30
60
9
12
y
y
x
5 3
60
x
30
x
45
y
Factoring: For #6-8, solve for each variable by factoring. (Remember to set = 0 first!)
6.) 3m2 – 48 = 0
7.) 3p2 + 5p = 2
8.) 2x3 - 4x2 = 30x
HW #24: (#9-14) Congruent Segments and Congruent Angles
Congruent Segments: For #9-10, construct a segment congruent to the given segment.
9.)
10.)
Congruent Angles: For #11-12, construct an angle congruent to a given angle.
11.)
12.)
13.)
14.)
HW # 25: (#15-21) Congruent Segments, Congruent Angles, and Perpendicular Lines
15.) Construct a segment congruent to the
given segment.
16.) Construct an angle congruent to the given
angle.
______________________
17.) Given a point on a line, construct the
perpendicular to the line at the given point.
18.) Given a point not on a line, construct the
perpendicular to the line from the given point.
______________________
____________________
19.) Given a point not on a line, construct a
perpendicular to the line through the given
point.
20.) The longer leg of a 30-60-90 triangle
measures 12m. Find the length of the shorter leg
and the hypotenuse.
21.) Taylor is constructing an angle
congruent to ABC . What is her next
step?
A. using MN as the radius, place the center of
the compass on P and construct an intersecting
arc
B. using MB as the radius, place the center of the
compass on P and construct an intersecting arc
A
M
B
C. using MN as the radius, place the center of
the compass on Y and construct an intersecting
arc
C
N
D. using MN as the radius, place the center of
the compass on X and construct an intersecting
arc
X
P
Y
HW #27: (#22-28) Review of Constructions
22.) Construct a segment congruent to the given
segment:
A
23.) The hypotenuse of a 30-60-90 triangle is 16m
long. Find the area of the triangle.
B
24.) Construct an angle congruent to the given
angle:
25.) Construct an angle congruent to the given
angle:
26.) Construct a perpendicular line to the segment
through the given point:
27.) Construct a perpendicular line to the segment
through the given point:
E
F
H
G
28.) Find the area of a regular hexagon with radius 10m.
J
I
HW#28: (#29-35) Parallel Lines and Segment Bisectors
29.) Construct the perpendicular bisector of the
given segment.
30.) Given a point not on a line, construct a
parallel to the line through the given point.
31.) Construct a segment congruent to the given
segment.
32.) Construct an angle congruent to the given
angle.
______________________________
33.) Given a point outside a line, construct the
parallel to the given line through the given point.
34.) Given a point outside a line, construct the
perpendicular to the given line through the given
point.
35.) Nicole is working on the following construction with her compass and straightedge. Which
best describes the construction that Nicole is doing?
A. a line through P parallel to line l
B. a line through P intersecting line l
P
C. a line through P congruent to line l
D. a line through P perpendicular to line l
HW#29: (#36-39) Angle Bisectors
36.) Construct the bisector of the given
angle.
37) Construct the bisector of the given
angle.
38.) Milon is working on the following construction with his compass and straightedge. What is he
constructing?
A. An angle bisector
B. An angle congruent to a given angle
C. A line parallel to a given line
Y
X
39.) Mitchell just constructed an angle bisector
of angle A. What was his first step?
D. A perpendicular bisector of a segment
A. Draw AD
B. Draw a line segment connecting points B and C
B
D
C. From points B and C, draw equal arcs that
intersect at D.
D. From point A, draw an arc that intersects the
sides of the angle at points B and C.
A
C
HW #30: (#40-48) Constructions Review
40.) Given a point outside a line, construct the
parallel to the given line through the given point.
41.) Construct a segment congruent to the given
segment.
______________________
D
42.) Construct the perpendicular bisector of the
given segment.
43.) Given a point outside a line, construct the
perpendicular to the line from the given point.
D
44.) Construct the bisector of the given angle
45.) Construct an angle congruent to the given
angle.
46.) Sarah just constructed an angle bisector of angle A. What was her first step?
A. Draw AD
B
B. Draw a line segment connecting points B and C
D
C. From points B and C, draw equal arcs that
intersect at D.
D. From point A, draw an arc that intersects the
sides of the angle at points B and C.
A
C
47.) Charlie is working on the following construction with his compass and straightedge. What is
he constructing?
A. A line parallel to a given line
B. A perpendicular to a line from a point not on the
line
C. A perpendicular bisector of a segment
P
C
D
D. A perpendicular to a line from a point on the line
48.) Anisha is constructing an angle bisector. What is her next step?
A. Draw XY
C
B. Place the center of her compass on X and
construct an arc in the interior of ABC . Repeat
from Y.
Y
A
X
B
C. Place the center of her compass on X and
construct an arc intersecting A. Repeat on Y, with
the arc intersecting C.
D. Place the center of her compass on A and
construct an arc in the interior of ABC . Repeat
on C.
HW#31: (#49-58) Right Triangle Review
Solve for the variables:
49.)
50.)
51.)
5
x
8
30
8
x
6
y
12
11
x
52.)
53.)
54.)
60
30
y
60
y
2 2
45
10
9
x
x
30
45
60
x
y
Solve each problem:
55.) Find the length of the diagonal of a square with 56.) Find the perimeter of a square with diagonal
perimeter 20m.
8 ft.
57.) Find the altitude of an equilateral triangle with
perimeter 18in.
58.) Find the perimeter of an equilateral triangle
with altitude 9m.