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WorksheetsUnit 4 Test Review
Total questions: 221
Worksheet time: 55hrs 15mins
State if the triangles are congruent or not. If they are, state how you know.
Yes - by SSS
Yes - by ASA
Yes - by HL
Yes - by AAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by SSS
Yes - by ASA
Yes - by HL
Yes - by AAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by SSS
Yes - by ASA
Yes - by HL
Yes - by AAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by SSS
Yes - by ASA
Yes - by HL
Yes - by AAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by SSS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by SSS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by AAS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by AAS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by AAS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
State what additional information is required in order to know that the triangles are congruent for the reason given.
RS≅QS
RS≅QD
∠QRS≅∠QDS
DS≅SQ
What are the five ways to prove triangles are congruent? #4
SSS, ASA, AAS, SAS, HL
SSS, SSA, HL, AAS, SAS
SAS, SSA, HL, AAS, SSS
HL, SAS, SSA, SSS, ASA
Which of the following cannot be used to prove triangles are congruent? #2
HL
AAA
SSS
SAS
Which triangle congruence theorem can be used to prove the triangles are congruent? #1
SAS
SSA
ASA
AAS
△TVX is equilateral. Complete the proof that △VWX≅△VUT. #14
AAS
ASA
CPCTC
Definition of Congruence
Congruent figures... #15
Have the same dimensions (side lengths and angle measures)
Are the same shape and size
Can be mapped onto one another using rigid motions
All of the above
Name the theorem that proves these triangles are congruent. #16
The two triangles are congruent. Find the value of c.
(Diagrams are not to scale.) #19
4
5
3
38
How are the two triangles congruent? #22
#23
What is the correct choice for Reason 3? #24
Why is ΔAEB ≅ ΔCED? #26
SAS
ASA
AAS
SSS
Name the theorem or postulate, if possible, that makes the triangles congruent. #5
SAS
ASA
AAS
Not Possible
State if the triangles are congruent and why. #6
AAS
ASA
Not congruent
SSS
For the triangles to be congruent by HL, what must be the value of x? #7
2
3
4
7
What is reason #4? #9
Which triangle congruence theorem proves that triangle PRS is congruent to triangle QRS? #17
State if the triangles are congruent or not. If they are, state how you know.
Yes - by AAS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
State if the triangles are congruent or not. If they are, state how you know.
Yes - by AAS
Yes - by ASA
Yes - by HL
Yes - by SAS
Not congruent
Which triangle congruence theorem can be used to prove the triangles are congruent?
SSS
SAS
ASA
NONE
Which triangle congruence theorem can be used to prove the triangles are congruent?
SSS
SAS
ASA
NONE
Identify the correct triangle congruence theorem.
ASA
AAS
Identify the correct triangle congruence theorem.
ASA
AAS
What is the correct choice for Statement 4?
⊿GHI ≅ ⊿JKL
⊿GHI ≅ ⊿KLJ
⊿GHI ≅ ⊿LJK
⊿GHI ≅ ⊿LKJ
What is the correct choice for Reason 5?
SAS
Definition of Congruence
Prove
CPCTC
Find the measure of the exterior angle.
12
76
128
180
In a geometric proof, reasons on the _____ side
Left
Right
transative
POE
In a geometric proof, statements go on the ____ side
left
right
transative
POE
If B is the midpoint of AC , then AB≅BC
Definition of midpoint
Definition of angle bisector
Definition of segment bisector
Definition of perpendicular lines
If m<1 + m<2 = 50 and m<2 = 10, then m<1 + 10 = 50
Transitive property
Substitution
Definition of angle bisector
Subtraction POE
The symbol ≅ means..........
Congruent
transitive
equal sign
supplementary
When writing a proof start with ......
The given
Transative property
Supplementary angles
Subtraction POE
Since segment BD is part of both triangles, it is congruent to itself, what do we call this?
Substitution
Commutative
Reflexive
CPCTC
In the given proof, what is the reason for step 2?
Alternate Exterior Angle are Congruent
Reflexive Property of Congruence
Angles that form a linear pair are supplementary.
Alternate Interior Angles are Congruent.
What does it mean to bisect a segment or an angle?
Split it into 3 equal parts.
Split it into 2 equal parts.
Split into 4 equal parts.
Double it.
What does CPCTC stand for?
Corresponding Parts of Corresponding Triangles are Congruent
Congruent Parts of Corresponding Triangles are Congruent
Corresponding Parts of Congruent Triangles are Congruent
Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2
Parallel
Perpendicular
Neither
If two lines are perpendicular to each other their slopes are ____________
the same.
negative reciprocals of each other.
PJ ≅ LR
Prove that PR ≅ LJ
Select the first statement and reason when writing the proof.
Statement: PJ ≅LR
Reason:
Given
Statement: PR ≅LJ
Reason:
Given
PJ ≅LR , Prove that PR ≅ LJ
PJ ≅LR
Given
PJ =LR
If two segments are congruent, they are equal in length.
JR =JR
Reflexive Property
PJ + JR = LR + JR
Addition property.
PR = LR
Substitution property.
m ∠ RST = m ∠ WTS
PS Bisects ∠ RST
PT Bisects ∠ WTS
Prove that m ∠ 1 = m ∠ 2
m ∠ RST = m ∠ WTS
1. Given
PS bisects ∠ RST
PT bisects ∠ WTS
2. Given
m ∠ 1 = 21 of m ∠ RST m ∠ 2 = 21 of m ∠ WTS
Definition of Angle Bisector
m ∠ 1 = m ∠ 2
Halves of equals are equal.
What is the "statement" for step 3 of the proof?
HA=HA
HA=AH
MA=AM
MA=MA
What is #4 Statement?
∠MNL ≌ ∠ONP
MN ≌ ON
N ≌ N
MO ≌ OM
What is #3 Reason?
Same Line
Perpendicular Lines
Segment Bisector
Reflexive Property
What is #3 Reason?
Alternate Exterior Angles
Alternate Interior Angles
Vertical Angles
Angle Bisector
Which of the following is a correct statement and reason for the proof shown?
∠GEQ≅∠NEW Vertical
WN≅GQ ; Prove
∠G≅∠N ; Alternate Interior
∠W≅∠Q ; Alternate Interior
Give the Reason for #1.
Given
Segment Addition Property
Addition Property of Equality
PQ + QR = PR
Transitive Property of Equality
If AB=BC and BC=CE then AB=CE.
Transitive Property of Equality
Segment Addition Postulate
Reflexive Property of Equality
Symmetric Property of Equality
What is the correct reason for
Reason #3?
Definition of a Straight Angle
Prove
Definition of a Supplementary Angles
Transitive Property
Name the property of equality or congruence that justifies this statement.
Symmetric
Transitive
Substitution
Reflexive
Definition of Supplementary Angles
Reflexive Property
Transitive Property
Symmetric Property
Congruent Line Segment Property
Addition Property of Equality
Definition of Midpoint
Reflexive Property of Equality
Symmetric Property of Equality
Addition Property of Equality
Substitution Property of Equality
Transitive Property
Angle A + Angle B = 90
Angle A + Angle B = 180
Angle A and Angle B are both obtuse angles
A mathematical statement that requires proof is a
theorem
postulate
definition
conjecture
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
State if the two triangles are congruent. If so, state how you know.
Congruent by SSS
Congruent by SAS
Not Congruent
What additional information is required for the two triangles to be congruent by SSS? #1
A
B
C
D
What additional information is required to prove the two triangles are congruent by SSS? #2
A)
B)
C)
D)
State if the two triangles are congruent. If they are, state how you know. #4
A
B
C
D
Why are these triangles congruent? #5
SSS
SAS
ASA
AAS
Find the value of x. #7
ΔABC≅ΔDEF , THE 2 TRIANGLES ARE ≅ BY SSS AND SAS
4
1
-5
-1/2
Are these triangles congruent by SSS? #8
Yes ΔACB≅ΔXYZ
No
Yes ΔCBA ≅ΔYXZ
Yes ΔCBA≅ΔYZX
Which statement will make ΔDNG ≅ ΔPNG by SSS? #9
N is the midpoint of DP
∠D≅∠P
PG ≅DG
GN ⊥ DP
#11
Which triangle congruence theorem can be used to prove the triangles are congruent? #12
AAS
SSS
Not enough information given
ASA
What is Reason C? #22
SSS Congruence
SAS Congruence
ASA Congruence
AAS Congruence
HL Congruence
What is Reason B? #23
Definition of Right Angles
Definition of Perpendicular
Definition of Given
Definition of Right Triangles
Which triangle congruence theorem can be used to prove the triangles are congruent?
SSS
SAS
ASA
NONE
Which triangle congruence theorem can be used to prove the triangles are congruent?
SSS
SAS
ASA
NONE
<F = ___
acute
obtuse
right
acute
obtuse
right
A triangle with 3 congruent sides is called a(n) ______
Isosceles Triangle
Equilateral Triangle
Obtuse Triangle
Irregular Triangle
A triangle can be classified as an isosceles triangle if there are two equal sides.
True
False
Classify this triangle by its sides and angles.
acute & scalene
right & scalene
right & equilateral
acute & equilateral
Classify this triangle by its sides and angles.
obtuse & equilateral
obtuse & isosceles
right & isosceles
right & equilateral
Classify this triangle by its sides and angles.
obtuse & isosceles
right & scalene
right & isosceles
obtuse & scalene
Find the measure of the missing angle.
47
57
53
133
acute
obtuse
right
acute
obtuse
right
acute
obtuse
right
acute
obtuse
right
acute
obtuse
right
equilateral
isosceles
scalene
equilateral
isosceles
scalene
equilateral
isosceles
scalene
equilateral
isosceles
scalene
A triangle has side lengths of 15 centimeters, 11 centimeters, and 9 centimeters. What kind of triangle is it?
equilateral
isosceles
scalene
What is the measure of BC?
12
6
not enough information
10
A triangle with 3 congruent sides is called a(n) ______
Isosceles Triangle
Equilateral Triangle
Obtuse Triangle
Irregular Triangle
A triangle can be classified as an isosceles triangle if there are two equal sides.
True
False
Classify this triangle by its sides and angles.
obtuse & isosceles
obtuse & equilateral
right & isosceles
right & equilateral
The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. #18
Solve for x. #6
x = 7
x = 8
x = 6
x = 9
Find the measure of angle A. #2
Solve for x. #8
What is the measure of angle A in the triangle? #4
Find m ∠B. #10
150°
67°
54°
57°
Solve for x. #13
(a)
Fill in statement #2. #30
m∠6+m∠2+m∠3+m∠5=360
m∠1+m∠4=m∠6
m∠1+m∠2+m∠3=180
m∠1+m∠4+m∠7=180 (This is the correct answer!)
In the formal proof of the triangle sum theorem, the triangle is always formed between ________________________. #31
perpendicular lines
parallel lines (This is the correct answer!)
intersecting lines
a bunch of points
Find the missing angle in the figure.
50°
130°
30°
80°
Find the missing angle in the figure.
72°
53°
52°
108°
Use the triangle to solve for x, and then find the measure of angle A.
5°
39°
80°
41°
Solve for x.
(a)
Find x.
(a)
Find the ?
(a)
Find the measure of each angle indicated.
(a)
Find the measure of each angle indicated.
(a)
What is the value of x?
(a)
If an isosceles triangle has a base angle measuring 40°, then what measure is the VERTEX angle?
120°
100°
40°
80°
What is the measure of BC?
12
6
9
10
If AE≅DE, then ∠A ≅∠ ?
B
C
D
E
Solve for the value of X.
X= (a)
What should be the value of x, y and z?
x=43°
y=10
z=10
x=43°
y=10
z=5
x=47°
y=10
z=5
x=47°
y=10
z=10
9
10
6
11
Solve for x.
-6
-11
12
-12
SOLVE FOR X
10
-12
-10
6
What is the
m∠U ?
(a)
What is the measure of
EF ?
(a)
What is the name of this kind of triangle?
Right
Isosceles
Scalene
Equilateral
What is the name of this kind of triangle?
Right
Scalene
Isosceles
Equilateral
9
10
6
11
What is the measure of ∠A?
46
134
90
88
What is the measure of BC?
12
6
not enough information
10
