Download A 2. Construct the line perpendicular to line l through point A

1. Construct the perpendicular bisector of the segments below.
using smaller arcs
Name ____________________ Date ________________
CC Geometry R
HW #9A Constructing a Perpendicular Bisector
using larger arcs
L
A
B
M
2. Construct the line perpendicular to line
l through point A.
Number the steps in the correct order, from 1 - 5.
3
A
5
4
2
l
1
Draw circle(arc) B: center B and
circle C(center C), using two
equal radii that intersect.
Draw AD.
Label D, the intersection of arcs
B and C.
Label the two points of intersection
as B and C.
Draw circle(arc)A: center A,
intersecting l in two points.
3. Construct the perpendicular bisectors of AB, BC , and CA on the triangle below.
What do you notice about the segments you have constructed?
The three perpendicular bisectors intersect in the same point. They are CONCURRENT.
A
B
C
OVER
4. Two homes are built on a plot of land. Both homeowners have dogs, and are
interested in putting up as much fencing as possible between their homes on the
land, but in a way that keeps the fence equidistant from each home. Use your
construction tools to determine where the fence should go on the plot of land.
perpendicular
bisector
H2
of H1H2
H1
Review
2
5. In ΔABC, ≮B = ≮C. If AB = x + 8x and AC = 20.
a) Label the diagram.
b) Write and solve a quadratic equation for x. There will be two answers.
A
2
x + 8x = 20
x2 + 8x
20
x = ­10 / x = 2
B
C
c) If BC = 3x + 5, choose the appropriate value for x, and find the perimeter of
Perimeter = 20 + 20 + 11 = 51
BC = 3x + 5 ΔABC.
BC = 3(2) + 5 = 11
6. Find x, and classify the triangle
by its angles.
co
78o
(2x+4)o
65o
(2x­9)o
7) Find the variables.
a
83o
do
o
bo
37oxo
fo
1260
(2x + 4) + (2x ­ 9) + x = 180
5x ­ 5 = 180
go
5x = 185
x = 37 eo
56o
54 c = ____
34
43 b = ____
a = ____
acute triangle
27 e = ____
110
126 g = ____
27 f = ____
d = ____
Aim/Hwk 9B
Construction Practice
Math 10X
Name____________________________________
Show all construction marks.
1. Construct and label the perpendicular bisector XY of AB.
B
A
2. Construct and label equilateral ΔABC using segment DE as a side length.
D
E
60°
A
3. Construct and label bisector QS of
PQR
P
Q
S
R
4. Construct and label ≮ XYZ equal in measure to ≮ ABC.
X
A
B
C
Y
Z
0
5. Construct ≮HEF which measure 30 .
angle bisector of 60O
H
60°30°
F
E
6. Construct a line perpendicular to the
given line through the given point P.
Clearly and precisely list the
steps needed to accomplish this
construction.
1. Draw circle (arc) P, center P, any radius, intersecting the line in two points.
P
2. Label the points A and B.
3. Draw circle A, center A, radius AP and circle B, center B, radius BP.
A
B
4. Label C, the intersection of circles A and B.
5. Draw line PC.
C
7. Construct a right angle with vertex P.
P
8. Construct a line parallel to the given line through the given point P.
P
9. In the space below to the right , construct and label≮ABC whose
measure is one-half the measure of≮UVW.
A
U
V
B
W
0
10. Construct and label ≮RST which measures 45 .
45°
S
C
11. Construct and label equilateral ΔCDE such that CD = 2AB.
D
A
C
B
E
12. Solve for x and y. Show work.
4x ­ 10 = 90 y = 180 ­ 24
4x = 100
y = 156
240
y
x = 25
4x ­ 10
y
13. Construct three more equilateral triangles
that each share a side withΔABC.
C
A
B
14. True or false? If false, correct the sentence so that it is always true.
F Alternate interior angles are equal.
a) ____
If parallel lines are cut by a transversal, alternate interior angles are =.
0
F
b) ____The sum of an angle and its supplement is 90o.
180
cannot
F A scalene triangle could be isosceles.
c) ____
180o
F The sum of theadjacent angles on one side of a line is 3600.
d) ____
T A line segment has an infinite number of bisectors.
e) ____
15. State the reason that justifies the statement.
a) m≮ABC = m≮ABD + m≮DBC
Angle Addition Postulate
C
D
diagram for a.
B
A
b) m≮VSB = m≮LBS
If ll lines are cut by a transversal, alternate interior angles are equal.
R
c) m≮RST = m≮SBL
If ll lines are cut by a transversal, corresponding angles are equal.
T
S
V
diagram for
d) m≮RST = m≮VSB
b - e.
L
B
Vertical angles are equal.
0
e) m≮TSR + m≮RSV = 180
Angles that form a linear pair sum to 180o.
16. Fill in the blanks.
line
a) Collinear points are points that lie on the same ___________.
half plane
b) A ________-_________
is the set of all points in a plane on one side of a line.
equiangular (all angles equal)
c) A regular polygon is both equilateral and _____________________.
Deductive
d) _________________reasoning
is reasoning based on observations and accepted
facts.
e - h Fill in a number.
0 midpoint(s).
e) A line has ____
1 perpendicular bisector(s).
f) A segment has _____
1 midpoint(s).
g) A segment has ____
1 bisector(s).
h) An angle has ____
17. Solve for y. Show work.
5y
2y­30
y+102
7y ­ 30 = y + 102 (Exterior angle Th.)
6y = 132
y = 22