Download Geometry 1st Semester Review

Geometry 1st Semester Review
Name________________________________#_____
YOU MUST SHOW ALL WORK TO RECEIVE CREDIT. YOU MAY USE SEPARATE PAPER, BUT IT MUST BE
ATTACHED.
Use the diagram at right for questions 1-4.
1.
A
Give 2 ways to name a line containing point A.
2.
Name 2 points that are collinear with point D.
3.
Name 2 points that are NOT collinear with points C and B.
4.
Name a plane passing through points F, C, and E.
F
C
D
B
E
K
m
Use the figure at right for questions 5 –7.
5.
Name all the lines that intersect at E.
6.
Name a plane parallel to ABG
7.
Name a line that is skew to AF .
B
C
G
A
H
D
F
E
Answer questions 8-12, given that R(-3, -4) and S(5, 7).
8.
What is the midpoint of RS .
9.
What are the coordinates for point U if S is the midpoint of RU .
10.
What is the slope of RS ?
11.
What is the slope of a line perpendicular to RS ?
12.
Find RS.
13.
AB = 3x + 6, BC = 2x + 14, and B is the midpoint of AC . Find AC.
14.
AC = 3x - 1, BC = 12 - x, and B is the midpoint of AC . Find AB.
15.
L is between M and P. LP = x, MP = 27, and ML = 4x – 3. Find x.
16.
L is between M and P. ML = 13, LP = x – 1, MP = 3x + 6. Find x.
Use the figure at right for questions 17 - 20.
17.
m CHA = (4x + 1) , m SHA = (2x – 2) m CHS = 125 . Find x.
18.
m CHA = 25 , m SHA = (2x + 6) m CHS = (5x + 4) . Find x.
19.
HA is an angle bisector, m SHA = (5x – 4) , and m CHS = (x + 37) .
Find m CHA.
C
H
A
S
20.
HA is an angle bisector. m CHA = (5x + 7) , and m CHS = 87 . Find x.
Use the diagram at right for questions 21 –27.
21.
What kind of angle pair is 2 and 3?
If m // n , m 2 = (3x + 12) and m 3 = (4x – 7) . Find x.
22.
What kind of angle pair is 7 and 5?
If m // n , m 7 = (16x – 20) and m 5 = (13x + 7) . Find x.
23.
1
2
8
m
3
What kind of angle pair is 8 and 7?
If m // n , m 8 = (6x) and m 7 = (13x - 10) . Find x.
7
4
6
n
5
24.
What kind of angle pair is 1 and 5?
If m // n , m 1 = (4x - 5) and m 5 = (3x + 11) . Find x.
25.
What kind of angle pair is 2 and 4?
If m // n , m 2 = (7x - 12) and m 4 = (3x) . Find x.
26.
What kind of angle pair is 8 and 5?
If m // n , m 8 = (8x + 40) and m 5 = (6x) . Find x.
27.
What kind of angle pair is 1 and 6?
If m // n , m 1 = (3x + 18) and m 6 = 108 . Find x.
28.
The measure of an angle is 6 more than 3 times its complement. Find the measure of both angles.
29.
The measure of an angle is 18 less than 8 times its supplement. Find the measure of both angles.
30.
Write the equation of a line that passes through (4, 10) and is parallel to the line with the
equation y = -3x + 7.
31.
Write the equation of a line that passes through (6, -5) and is perpendicular to the line with the
equation y = -2x – 9.
Use CHS at right for questions 32 – 35.
32.
33.
If HA is an altitude, what is the m HAS?
If SH is an altitude with slope of
C
3
, what is the slope of CH ?
4
H
34.
CP is a median, HP = 3x + 9 and HS = 8x – 4. Find x.
35.
MO is a perpendicular bisector of CS . If m OMS = (16x – 38) , find the value of x.
36.
Determine the order of the SIDES from shortest to longest.
a.
b.
P
A
63
G
52
65
I
H
47
93
43
M
M
O
S
37.
If the perimeter of ΔCAT = 84, CA = 2x + 7, AT = 5x + 6, and CT = 6x – 20, determine the order the
ANGLES from largest to smallest.
38.
Determine the order of the ANGLES from smallest to largest.
P
a.
b.
12
G
A
93
50
34
H
I
43
M
77
39.
In ΔCAT, m C = (7x + 10) , m A = (3x + 14) , and m T = (6x + 20) , determine the order the SIDES from
longest to shortest.
40.
Determine if the measures can form the sides of a triangle.
a. 70, 79, 18
b. 72, 5, 77
c.
14, 90, 25
41.
Given 2 sides of triangle, between what 2 numbers must the measure of 3rd side fall.
a. 37 and 16
b. 5 and 23
c. 41 and 28
42.
What is the longest side in the figure.
L
25
F
43.
What is the longest side in the figure.
I
60
T
56
89
82 43
48
73
34
76
64
70
A
T
R
E
44.
Write the inverse of the statement, “If two angles are vertical, then they are congruent.” Determine if
the inverse is true or false.
45.
Write the converse of the statement, “If two angles are vertical, then they are congruent.” Determine if
the converse is true or false.
46.
Write the contrapositive of the statement, “If two angles are vertical, then they are congruent.”
Determine if the contrapositive is true or false.
47.
Give a counterexample to show that the statement below is false.
“If two angles are supplementary then one of the angles is acute and the other is obtuse.”
48.
A biconditional must contain what phrase?
49.
Given that the statement below is of the form p
kind of statement called?
50.
q, write the statement p
“If angles form a linear pair, then they are supplementary.”
Name the algebraic property: If JK – 3 = PQ + 4, then JK = PQ + 7.
q in words. What is this
51.
Name the algebraic property: If m ABC = m DEF, then m DEF = m ABC.
52.
Name the algebraic property: If m A = 45 and m A + 40 = m B, then 45 + 40 = m B.
53.
Complete the statement using the reflexive property: AB = ____________.
54.
Complete the statement using the subtraction property: If m JHK + 30 = 120, then ______________.
55.
Complete the statement using the definition of midpoint: If A is the midpoint of
BC , then _________.
56.
Complete the statement using the definition of congruent statements: If
PR , then ___________.
57.
If
58.
In the conditional, “If two angles are right angles, then they are congruent,” identify the hypothesis and
conclusion.
59.
Classify the triangle below by its angles and sides.
LM
AC and DE intersect at B and m ABD = 41 – x and m CBE = 5x – 13, find x.
50
40
60.
Classify the triangle below by its angles and sides.
98
41
61.
In ABC, m A = m B = m C, classify the triangle by its angles and sides.
62.
In ABC,
63.
In DEF, m E = m F = 60 . DF = 7 – 2x and the perimeter of DEF = 51. Find x.
64.
In isosceles triangle, GHI,
65.
In the figure below, m ABD = (7x + 9) , m D = (6x) , and m C = (42 – 2x) . Find x.
AB
BC , and m B = 90 . and m A=(4x + 1) . Find x.
A
B
I is the vertex angle and m G = 72 . Find m I.
C
D
66.
Complete the congruence statement, ABC
B
D
A
C
E
___________ by ____________.
67.
Complete the congruence statement, ABC
B
D
A
68.
___________ by ____________.
C
Complete the congruence statement if ADC is an isosceles triangle with vertex angle,
ABC ___________ by ____________.
B
D, and
E
D
A
69.
70.
ABC
C
DEF, m A = (5x) , m B = 85 , m F = 65 . Find x.
Complete the statement :
ADB
CDB because
C
B
A
________________________________________
________________________________________
________________________________________
71.
Complete the congruence statement:
A
ABC
D
_____________ by ______________.
B
C
D
72.
In quadrilateral ABCD, m A = 90 , m B = 94 , m C = (4x – 2) , and m D = (5x + 34) . Find x.
73.
Draw a regular convex octagon.
74.
Draw a concave heptagon.
75.
Determine which of the following is a parallelogram.
(a)
(b)
(c)
(d)
AE
CB .
76.
ABCD is a parallelogram. m B = (13x + 27) , m C = 49 . Find x.
77.
If EFGH is a parallelogram, complete each statement.
F
G
a)
FEH
______________
b) FG = _________________
c) FJ = __________________
J
E
d)
H
HEG
______________
e) m GFE + ______________ = 180
78.
DEFG is a parallelogram. m D = (3x + 14) , m G = (5x – 38) , m E = y , m F = (2z) . Find x, y, z.
79.
How do you know that RSTU is a parallelogram?
S
T
R
U
For questions 80-83, write the two column proof.
80.
Given:
x // y
81.
1
1
4
Prove: p //m
3
x
5
y
4
p
H
M
K
5
6 7
8
J
L
(11 Steps)
Given: C is the midpoint of
B
E
Prove: DBC
AEC
(5 Steps)
GH // KL
Prove: 5 & 8 are
supplementary
m
( 5 Steps)
82.
G
Given: HJ // LM
83. Given:
BE
D
BD AC
BD bisects ABC
Prove:
B
(8 Steps)
C
E
A
A
B
C
A
D
C
Geometry 1st Semester Review Answers
1.
2.
3.
4.
m, AD
5.
6.
DE , GE , FE
FHE
7.
BC GC DE HD
8.
9.
10.
B & C, or F & E
F, E, or A
K or FCE
1,
31.
y
32.
90
33.
3
2
(13, 18)
11
11
12.
13.
14.
15.
16.
17.
18.
19.
185
x=8, 60
x=5, 7
6
3
21
9
x=5, 21
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
7.3
linear pair, 25
vertical, 9
CIA, 10
AEA, 16
CA, 3
none, 10
none, 18
69 , 21
22 , 158
y = -3x + 22
80.
a.
a.
b.
c.
d.
x // y
a.
HJ
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
GH // KL
1
4
1
4
4
3
p //m
// LM ,
6
8
m 6=m 8
5
7
m 5=m 7
6 & 7 are supp.
m 6 + m 7 = 180
m 8 +m 7 = 180
m 8 + m 5 = 180
5 & 8 are supp.
2
x
53.
54.
55.
56.
57.
58.
8
4
3
11
8
36.
PI , GI , PG
37.
38.
HA , HM , AM
C, A, T
I, P, G
39.
40.
CA , AT , CT
Y, N, N
41.
21 & 53
18 & 28
13 & 69
42
FT
H,
8
1
34.
35.
8
11.
81.
Name________________________________#_________
A,
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
M
71.
72.
73.
43. TI
44. If two angles are not vertical, then
they are not congruent; FALSE
45. If two angles are congruent, then
they are vertical; FALSE
46. If two angles are not congruent,
then they are not vertical; TRUE
47. Two right angles
48. “if and only if”
49. If angles do not form a linear pair,
then they are not supplementary;
INVERSE
50. Addition Property
51. Symmetric Property
52. Substitution Property
a.
a.
b.
c.
d.
Given
Given
// CA
Transitive
AIA  //
a.
Given
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
Given
// CA
Defn
// CA
Defn
Linear Pair Postulate
Def supp ’s
Substitution
Substitution
Def supp ’s
82.
83.
a.
B
74.
75.
76.
77.
78.
79.
AB
m JHK = 90
BA = AC
LM = PR
x=9
Hyp: two angles are right angles;
CONC: they are congruent
right, scalene
isosceles, obtuse
equiangular, equilateral, acute,
isosceles
x = 11
x = -5
m I = 36
x = 11
EBD; ASA
DCB; AAS
CEA; SAS
x=6
CBD
ABD by SAS or SSS, so
ADB
CDB by CPCTC
DCB; HL
x = 16
8 sides, all angles and sides marked
congruent
7 sides, with at least one side
“caved in”
C
x=8
(a) FGH (b) EH (c) JH (d) FGE
(e) m FGH or m FEH
x = 25.5, y = 89.5, z = 45.25
RS TU by CPCTC. If a
quadrilateral has one pair of opp.
sides that are both and || then it
is a parallelogram.
a.
Given
b.
C is the midpoint of BE
E
b.
Given
c.
d.
d.
e.
BC
c.
d.
d.
e.
Def. of midpoint
Def. of vertical angles
Vertical s
ASA
a.
BD
a.
Given
a.
b.
c.
d.
BD bisects ABC
BDA, BDC are right
BDA
BDC
ABD
CBD
a.
b.
c.
d.
Given
Def. of
All rt. s
Def. of bisector
e,
f.
g.
BD BD
ABD
CBD
A
C
e.
f.
g.
Reflexive Prop
ASA
CPCTC
EC
DCB and ACE are v.
DCB
ACE
DBC
AEC
AC
s