Download Unit 4 Review Packet

Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 1
Date: ___________________________
Part 1 – Polygons Review
1) Answer the following questions about a regular decagon.
a) How many sides does the polygon have? 10
b) What is the sum of the measures of the interior angles? 1440
c) What is the measure of each interior angles? 144
d) What is the sum of the measures of the exterior angles? 360
e) What is the measure of each exterior angle? 36
f) How many diagonals can be drawn in the polygon? 35
2) Each exterior angle of a regular polygon is 90. Answer each question about the polygon.
a) What is the sum of the exterior angles? 360
b) How many sides does the polygon have? 4
c) What is the name of the polygon? Quadrilateral
d) What is the sum of the measures of the interior angles? 360
e) What is the measure of each interior angle? 90
f) How many diagonals can be drawn in the polygon? 2
3) The sum of the interior angles of a regular polygon is 540. Answer each question about
the polygon.
a) How many sides does the polygon have? 5
b) What is the name of the polygon? Pentagon
c) What is the measure of each interior angle? 108
d) What is the sum of the measures of the exterior angles? 360
e) What is the measure of each exterior angle? 72
f) How many diagonals can be drawn in the polygon? 5
Part 2 – Segments in Triangles - Give the most specific name for each dotted segment.
Altitude
Perpendicular Bisector
Angle Bisector
Median
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 2
Date: ___________________________
Part 3 – Determine whether the triangles are congruent. If they are, name the congruent triangles and the
postulate or theorem you used. If there is not enough information, write none. Mark your diagrams.
D
AC ^ DB
L
K
H
G
A
C
B
LM // PN
LP // MN
F
KF // HJ
G is the midpoint of FH
DABD @ DCBD
HL
P
J
DKGF @ DJGH
AAS or ASA
Q
N
M
DLPN @ DNML
ASA
X
R
F
Y
W
T
S
G
H
J
Z
V
S is the midpoint of RT
A
None
DWXY @ DBZA
SSS
AD // BC
D
A
FG // JH; FG @ JH
B
DFGH @ DHJF
SAS
D
V
C
C
T
B
S
W
VT bisects SVW
A
None
None
CB @ DA
DDAC @ DBCA
HL
B
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 3
Date: ___________________________
Part 4 - Solve each algebra connection problem. Answer all questions.
2.
1.
A
2x
3x - 19
B
C
6x + 15
104°
A
B
x = 19
Classify the triangle by its sides: Isosceles
mA = 38
What two sides are congruent? AB = AC
mC = 38
What two angles are congruent? mB = mC
Classify the D by its sides: Isosceles
x=8
Classify the D by its angles: Obtuse
mC = 63
B
102°
48°
C
6x + 15 = 9x – 9
24 = 3x
x=8
2x + 3x – 19 + 104 = 180
5x = 95
x = 19
3.
9x - 9
C
mB = 63
4.
mA = 54
B
15x - 30
A
A
mA = 30
Are any of the angles congruent? No
Therefore, are any of the sides congruent? No
Classify the triangle by its sides: Scalene
Classify the triangle by its angles: Obtuse
Order the side lengths from longest to shortest:
Longest: AC
Middle: AB
Shortest: BC
10x
3x + 42
C
15x – 30 + 10x + 3x + 42 = 180
28x + 12 = 180
x=6
x=6
mA = 60
mB = 60
mC = 60
Classify the D by its sides: Equilateral
Classify the D by its angles: Equiangular
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 4
Date: ___________________________
NOTE: Many pieces of notation (such as segment bars and rays are missing).
Given: B is the midpoint of CA;
Statements
Reasons
DC @ DA
1) B is the midpoint of CA
1) Given
2) CB = BA
2) Definition of a Midpoint
3) DC = DA
3) Given
4) DB = DB
4) Reflexive
5) DCBD @ DABD
5) SSS
6) 5 @ 6
6) CPCTC
Prove: 5 @ 6
D
5 6
1
2
C
3
4
B
A
C
1
Statements
2
Reasons
1) D is the midpoint of AB
1) Given
2) AD = DB
2) Definition of a Midpoint
3) CA = CB
3) Given
4) CD = CD
4) Reflexive
5) DADC @ DBDC
5) SSS
6) 1 @ 2
6) CPCTC
7) CD bisects ACB
7) Definition of a Angle Bisector
A
D
B
Given: D is the midpoint of AB;
CA @ CB
Prove: CD bisects ACB
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 5
Date: __________________________
Statements
Given: AC @ DB; CD @ BA
Reasons
1) AC = DB; CD = BA
1) Given
2) AD = AD
2) Reflexive
3) DACD @ DDBA
3) SSS
4) C @ B
4) CPCTC
Prove: C @ B
C
A
D
B
Given: AC @ DB; CAD @ BDA
Statements
Reasons
1) AC = DB; CAD @ BDA
1) Given
2) AD = AD
2) Reflexive
3) DACD @ DDBA
3) SAS
4) CD = BA
4) CPCTC
Prove: CD @ BA
C
A
D
B
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 6
Date: __________________________
Statements
Reasons
Given: PR bisects QPS; PQ @ PS
Prove: RP bisects QRS
1) PR bisects QPS
1) Given
2) QPR @ SPR
2) Definition of an Angle Bisector
3) PQ = PS
3) Given
4) PR = PR
4) Reflexive
5) DPQR @ DPSR
5) SAS
6) QRP @ SRP
6) CPCTC
7) RP bisects QRS
7) Definition of an Angle Bisector
Q
P
R
S
Given: PR bisects QPS and QRS
Statements
Prove: RQ @ RS
Reasons
1) PR bisects QPS
1) Given
2) QPR @ SPR
2) Definition of an Angle Bisector
3) RP bisects QRS
3) Given
4) QRP @ SRP
4) Definition of an Angle Bisector
5) PR = PR
5) Reflexive
6) DPQR @ DPSR
6) ASA
7) RQ = RS
7) CPCTC
Q
P
R
S
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 7
Date: __________________________
Statements
Given: AB // DC; AD // BC
Reasons
Prove: DABC @ DCDA
1) AB // DC
1) Given
2) 1 @ 2
2) If lines are parallel, then alternate
interior angles are congruent.
3) AD // BC
3) Given
4) 3 @ 4
4) If lines are parallel, then alternate
interior angles are congruent.
5) AC = AC
5) Reflexive
6) DABC @ DCDA
6) ASA
B
A
4
1
2
D
3
C
Given: JL ^ KM; L is the midpoint of KM
Statements
Prove: DJLK @ DJLM
Reasons
1) JL ^ KM
1) Given
2) 2 and 3 are right angles
2) Definition of
Perpendicular Lines
3) m2 = 90; m3 = 90
3) Definition of Right Angles
4) m2 = m3
4) Substitution
5) L is the midpoint of KM
5) Given
6) KL = ML
6) Definition of a Midpoint
7) JL = JL
7) Reflexive
8) DJLK @ DJLM
8) SAS
J
K
1
2 3
L
4
M
Geometry/Trig 2
Name: __________________________
Unit 4 Review Packet – page 8
Date: __________________________
Statements
Given: TM @ PR; TM // RP
Reasons
Prove: E is the midpoint of TP
1) TM = PR
1) Given
2) TM // RP
2) Given
3) T @ P; M @ R
3) If lines are parallel, then
alternate interior angles are
congruent.
4) DTEM @ DPER
4) ASA
5) TE = EP
5) CPCTC
6) E is the midpoint of TP
6) Definition of a Midpoint
T
E
R
M
P
Given: C & D are right angles; AD @ BC
Statements
Prove: DBAD @ DABC
Reasons
1) C & D are right angles
1) Given
2) AD = BC
2) Given
3) AB = AB
3) Reflexive
4) DBAD @ DABC
4) HL
D
A
C
B