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Review Sheet Aims 1-11
1. Name an angle described by each of the following:
OB
a. a ray opposite OE: _____
B
A
O
≮EOA
________
b. a pair of vertical angles: ________
≮BOC
C
≮DOB
c. an angle that forms a linear pair with ≮EOD: __________
≮COE
d. two angles that are supplementary: ________
E
D
≮EOA
________
≮EOA
≮DOE
e. two angles that are complementary: ________
________
line
half-plane
regular
Deductive
angle bisectors
vertices
0
infinitely many
1
1
1
4. In the figure to the right, AB || CD.
a. Name an angle equal in measure to ≮3.
B
≮5
3
b. Name an angle equal in measure to ≮1. ≮7
1 2
A
c. Find two angles that are equal in measure to ≮2.
d. If m≮2 = 70 and m≮4 = 50, find m≮5. 60
0
D
≮6, ≮8
5
4 6
8 7
C
e. If m≮7 = 125 and m≮3 = 35, find m≮4. 900
5. In the figure to the right, CD bisects ≮ACB,
C
AB = BC, ≮BEC = 90 , and ≮DCE = 42 .
0
0
Find the measure of ≮A. 320
420
A
D
B
E
0
4x - 10 = 90
x = 25
y = 180 - 24
y = 156
7. Solve for y. Show work.
2y2 + 11y - 30 = y + 102
2y2 + 10y - 132 = 0
y2 + 5y - 66 = 0
(y + 11)(y - 6) = 0
y = -11 / y = 6
b. Find x so that m || n. Identify the
n
m
reason used.
2x + 45 + 3x = 180
5x = 135
2x + 45
3x
x = 27
3x
Vertical angles are equal.
If two lines are cut by a transversal such
that same side interior angles are
supplementary, then the lines are
parallel.
11y
2y2-30
y+102
8. Find and in each figure below. Justify your solutions by stating
appropriate facts, theorems or properties.
a.
b.
c.
720
450
560
72
0
73
45
0
0
730
560
Linear pairs form supp. ≮s. (720) If parallel lines are cut by a trans.,
Consecutive adjacent ≮s on a
same side interior ≮s are supp.
line sum to 1800. (500)
(x = 730)
If parallel lines are cut by a trans., Vertical angles are = . (730)
alternate interior ≮s are =.
The degree measure of the ≮s in
(y = 560)
a triangle sum to 1800. (y = 390)
If parallel lines are cut by a trans.,
corresponding ≮s are =.
(x = 520)
If parallel lines are cut by a trans.,
alternate interior ≮s are =.
109 - 64 = 45 (x = 450)
x = y (y = 450)
9. In the figure below, AD is the angle bisector of ≮BAC. BAP and BDC are
straight lines and AD ll PC.
Prove: AP = AC
Statements
1. AD ll PC
1. Givens
AD is the ≮bis.
y
z
w
Reasons
x
of ≮BAC
2. w = x
2. If ll lines are cut by a trans., corr. ≮s are =.
3. z = y
3. If || lines are cut by a trans., alt. int. angles are =.
4. w = z
4. An angle bisector divides an ≮ into 2 = parts.
5. x = y
5. Substitution Property of Equality
6. AP = AC
6. If two angles of a ∆ are =, the sides opposite the
angles are =.
Sometimes - true only if lines cut by a transversal are parallel.
Sometimes - true only if the angles are adjacent (share a common side).
Never
Always
Never
Sometimes - true only if the triangle is obtuse.
Use only a compass and straightedge. Show all construction marks.
11. Construct a line parallel to AB distance d from line AB.
d
d
A
B
12. Locate, by construction, the point I, equidistant from the three
B
I
A
C
incenter
What special point is I? _________________________
13. Make a copy of ≮IAC in the space below.
I'
A'
C'
of ΔABC.
14. Locate the point, H, equidistant from the three
of ΔABC.
Draw the circumscribed circle using your compass.
B
A
C
H
750
H
F
300
30
450
0
600
E
16. Construct a line perpendicular to
the given line through the given point P.
P
B
A
C
Clearly and precisely list the
steps needed to accomplish this
construction.
1. Draw circle P: center P, radius any size.
2. Label A and B, the intersection of circle P and
the line.
3. Draw circle A: center A, radius AB.
4. Draw circle B: center B, radius BA.
5. Label C, the intersection of Circles A and B.
6. Draw PC.
1350
C
450
A
900
B
Z
U
V
W
E
A
B
C
D
Clearly and precisely list the
steps needed to accomplish this
construction.
1. Draw circle A: center A, radius AC.
2. Draw circle B: center B, radius BA.
E
3. Label D, the unlabeled intersection
of circles A and B.
F
C
4. Draw circle C: center C, radius CA.
A
5. Label E and F, the intersections of
circle C with circles A and B.
B
6. Draw AE, EC, CF, BF, AD, and BD.
(Draw EF, DF, ED.)
D
22.
If m≮1 + m≮2 = 180, prove that a || c.
Statements
m
1
a
5
4
3 2
b
c
Reasons
1. ≮1 + ≮2 = 1800.
1. Given
2. ≮3 + ≮2 = 1800.
2. Linear pairs sum to 1800.
3. ≮1 + ≮2 = ≮3 + ≮2.
3. Substitution Property of
4. ≮1 = ≮3
4. Subtraction Property of
Equality
Equality
4. a ll c
5. If two lines are cut by a
transversal such that
corresponding angles are =,
the lines are ll.