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Construction WS #3
Name______________________Per.____
Geometry A
On a separate sheet of typing paper, perform the following constructions and then compare the triangles you’ve
created with your partners by holding them up to the light and see if they are congruent triangles.
Show all construction marks!!!
1) Construct
ABC
with
A , B and length AB
A
B
A
2) Construct
E
3) Construct
O
4) Construct
B
EFG
with the following segments:
F
F
OLN with the following measures for angles and segments.
L
O
N
O
QRS with the following measures for angles and segment.
S
Q
E
G
G
R
R
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Geometry A
Name ________________________
Triangle Congruence
Period _______
Determine whether the following triangles are congruent. If they are congruent, write the theorem or
postulate vertically, justifying each part of the theorem or postulate, and complete the triangle
congruence statement. NOTE: these figures are not drawn to scale!
1.
BCA   __________
B
_____  ___________  ___________
E
_____  ___________  ___________
_____  ___________  ___________
A
C
D
F
Justification: _______________
2.
MOP   __________
M
A
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
P
O
R
Justification: _______________
3.
A
DON   __________
O
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
J
N
D
Justification: _______________
2
4.
Y
GEO   __________
O
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
R
T
E
Justification: _______________
G
5.
B
C
ABD   __________
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
A
6.
D
B
I
Justification: _______________
BIE   __________
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
Justification: _______________
K
E
ABC   __________
7.
_____  ___________  ___________
B
D
_____  ___________  ___________
_____  ___________  ___________
Justification: _______________
3
A
8.
C
E
G
H
EGH   __________
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
E
Justification: _______________
M
9.
PAW   __________
M
_____  ___________  ___________
_____  ___________  ___________
A
W
C
_____  ___________  ___________
Justification: _______________
P
10.
B
C
ABD   __________
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
A
D
Justification: _______________
11.
P
N
MAP   __________
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
A
Justification: _______________
M
T
4
MAS   __________
12. Given : AS bisects MP; 1  2
A
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
Justification: _______________
1
2
M
P
13. Given : BD bisects ABC ; BD bisects ADC
B
ABD   __________
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
A
C
Justification: _______________
D
14. Given : MN || PT ; NO  TO
MNO   __________
P
N
_____  ___________  ___________
_____  ___________  ___________
O
T
_____  ___________  ___________
Justification: _______________
M
ABE   __________
15. Given: E is the midpoint of AD ;
A  D ; B  C
B
C
_____  ___________  ___________
_____  ___________  ___________
_____  ___________  ___________
Justification: _______________
A
E
D
5
Geometry A
Coordinate Proofs
NAME: _________________________
PERIOD: ___________
Show all your work on a separate sheet of E-2/graph paper!
Plot the
graph above and
information in
below:
Given: A (1, 8),
2) and M is the
Prove:
information given on the
then supply the missing
the two column proof
B (9, 12), C (-2, -2), D (6,
midpoint of
1. AB =
1.
Distance
Formula
2.
3.
4.
5.
6.
7.
CD =
M: (
)
BM =
MC =
BM = MC
Slope of
2. Distance Formula
3. Midpoint Formula
4. Distance Formula
5. Distance Formula
6.
7. Slope Formula
8. Slope of
8. Slope Formula
9.
9.
10.
10.
6
Plot the information given on the graph above and then supply the missing information in the two column
proof below:
Given: S (1, 7), M (12, 7), R (-5, -6), T (6, -6) and A is the midpoint of
Prove:
1. SM =
2. RT =
3. Slope of
=
1. Distance Formula
2. Distance Formula
3. Slope Formula
4. Slope of
=
4. Slope Formula
5.
5.
6.
6.
7.
7.
7
Plot the information given on the graph above and then supply the missing information in the two column
proof below:
Given: A (-3, 2), C (-9, -4), T (-2, -2), O (3, 2), G (2, -2) and D (9, -4)
Prove:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1. Distance Formula
2. Distance Formula
3. Transitive Property
4. Distance Formula
5. Distance Formula
6. Transitive Property
7. Distance Formula
8. Distance Formula
9. Transitive Property
10.
8
Name______________________Per._____
List the reasons for the following statements to complete each proof.
1. Given AB || CD ,
Prove: ABC 
AC || BD
DCB
#38
B
m
j
A
D
u
C
Statement
1. AB ||
Reason
CD
2. AC || BD
3. <ABC  < BCD
4. <ACB <DBC
5. BC  BC
6. ABC  DCB

2. Given:
Prove:
AD  BC, AB  DC
AD || BC
A
B
D
Statement
C
Reason
1. AD  BC
2. AB  DC
3. AC  AC
4. CAD  ACB

5. <DAC
< BCA
6. AD || BC
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#37 CPCTC
Name
1)
Per.___
a. Are the triangles congruent?
b. Why?
c. Is E  A ?
AR  ER
EC  CA
d. Why?
a. Is MES  OUS ?
2)
SE  SU
E  U
b. Why?
c. Is MS  OS ?
d. Why?
3)
a. Are the triangles congruent?
LK  UE
LU  UK
b. Why?
c. Is ULE  KUE
d. Why?
4)
FA|| TH
a. Are the triangles congruent?
b. Why?
c. Is AI  IT ?
d. Why?
5)
CI  IN
IO  IE
a. Is INO  ICE ?
b. Why?
c. Is ONI  ECI
d. Why?
10
Give the reason for each statement in the following proof.
A
B
6) Given: AD  BC, AB  DC
Prove: AD || BC
D
C
Statement
Reason
1. AD  BC
2. AB  DC
3. AC  AC
4. CAD  ACB

5. <DAC
< BCA
6. AD || BC
7. Write a two-column proof for the following.
Given: RY  AN : RN  AY
Prove: RYA  ANR
Statements
Reasons
1
1
2
2
3
3
4
4
5
5
8. Find the measure of the numbered angles ( 1-11) in order
6
2
58
1
71
4
5
9
7
8
3
11
61
10
1
2
3
4
5
6
7
8
9
10
11
11
CHAPTER 4 REVIEW
NAME ___________________Per.___
Do all work on e-2 paper in homework format
#39
st
1 = Write down the five ways you can prove two triangles to be congruent!!!!!
Identify as true or false. IF FALSE…re-write the statement making it correct

1. If ΔMNO
ΔXYZ, then MN  YZ .
2. A triangle that has only 2 congruent sides is classified as an isosceles triangle.


3. If ΔMNO
ΔXYZ, then / M
/ Y.
4. There are three shortcuts for showing that two right triangles are congruent.
5. Given ABC & DEF , if  A  D and  C  F and AC  DF , the postulate ASA can
be used to prove triangle congruency. (*hint: draw a picture)
6. There are five postulates/theorems to prove that non-right triangles are congruent:
SSS, SAS, ASA, AAA and AAS.
7. Given that isosceles triangle ABC  DEF , if <B and <E are the vertex angles and
m  A  x and m  F  y , then x = y. (*hint: draw a picture)
8. Equilateral triangles are also considered isosceles triangles.
9. If two right triangles are congruent, then their hypotenuses are also congruent.
10. Two scalene triangles will never be congruent.
11. State the theorem that can be used to prove, if possible, that the triangles are congruent.
a.
b.
c.
d.
J
H
H
G
J
K
G
F
e. B
E
E
f.
12
12. Find the measure of each angle a-h. The two lines with arrows are parallel.
a
c
125
d
g
b
110
f
125
e
115
a = _____
b = _____
c = _____
d = _____
e = _____
f = _____
g = _____
h = _____
h
13. Find the value of x.
x+1
a.
c.
b.
d.
92
45
x
70
3x - 4
2x + 1
x
40
x
23
14. Classify each triangle by its sides (scalene, isosceles, or equilateral) and its angles (acute, obtuse,
right, equiangular).
c.
b.
a.
15. Complete a 2-column proof:
Given: E is the midpoint of AD ;
A  D ; B  C
Prove: AB  DC
B
A
C
E
D
13
16. What additional congruency would you need in order to that the triangles are congruent by the
indicated method.
SAS_____________  ______________
AAS_____________  ______________
ASA_____________  ______________
HL _____________  ______________
17. Construct on your paper a triangle with given sides and included angle.
M
A
M
N
M
18. What is the measure of the exterior angle in the picture shown?
110o
19. Find the distance and slope between the points.
OH = _______________ slope = __________
H
OT = _____________
HT = ____________
O
slope = __________
T
slope = __________
14
Is this a right triangle?
How do you know?
What type of triangle is it?
20. If BOY  EAT , find the measure of the missing angles.
B
E
A
Y
O
27o
63o
T
m < B =___________ m < Y =_____________ m < E =_____________m < A =______________
21. Are the two triangles congruent? _________________ Why?___________________
Given: GM \ \OT
G
O
E
ME  EO
M
T
Is GE  ET ?_____________Why?___________________
15