Free Printable Triangle Congruence Theorems and Proofs Review

1.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

HL

b)

SSA

c)

SAS

d)

AAS

2.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

AAS

b)

SSS

c)

Not enough information given

d)

ASA

3.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

AAS

b)

SAS

c)

HL

d)

ASA

4.

Which of the following is NOT a triangle congruence theorem?

a)

HL

b)

SAS

c)

AAS

d)

AAA

5.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

AAS

b)

HL

c)

SSA

d)

AAA

6.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

ASA

b)

SSS

c)

SAS

d)

HL

7.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

Not enough information

b)

SAS

c)

SSA

d)

AAS

8.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

SSS

b)

SAS

c)

AAS

d)

ASA

9.

Which of the following proves congruence ONLY for right triangles?

a)

AAS

b)

HL

c)

SAS

d)

SSS

10.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

ASA

b)

SAS

c)

SSS

d)

Not enough information

11.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

AAS

b)

SSS

c)

SAS

d)

SSA

12.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

SAS

b)

Not enough information

c)

SSS

d)

AAS

13.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

HL

b)

AAS

c)

SAS

d)

AAA

14.

What is Reason D?

a)

SSS Congruence

b)

SAS Congruence

c)

ASA Congruence

d)

AAS Congruence

e)

HL Congruence

15.

What is Reason B?

a)

Definition of Congruence

b)

Definition of Equality

c)

Definition of Midpoint

16.

What is Reason F?

a)

SSS Congruence

b)

SAS Congruence

c)

ASA Congruence

d)

AAS Congruence

e)

HL Congruence

17.

What is Reason C?

a)

SSS Congruence

b)

SAS Congruence

c)

ASA Congruence

d)

AAS Congruence

e)

HL Congruence

18.

Which of the following is a correct statement and reason for the proof shown?

a)

$\angle GEQ\cong\angle NEW$ Vertical Angles Theorem

b)

$\overline{WN}\cong\overline{GQ}$ ; Definition of Midpoint

c)

$\angle G\cong\angle N$ ; Alternate Interior Angles Theorem

d)

$\angle W\cong\angle Q$ ; Alternate Interior Angles theorem

19.

Which of the following is a correct statement and reason for the proof shown?

a)

$\overline{DC}\cong\overline{DC}$ ; Reflexive Property

b)

$\angle A\cong\angle B$ ; Base Angles of Isosceles Triangle are Congruent

c)

$\angle1\cong\angle2$ ; Reflexive Property

d)

$\overline{AD}\cong\overline{DB}$ ; Definition of Bisect

20.

What is Reason C?

a)

Definition of Congruence

b)

Definition of Vertical Angles

c)

Reflexive Property

d)

Vertical Angle Theorem

21.

Complete the congruence statement.

a)

$\Delta CRP$

b)

$\Delta PCR$

c)

$\Delta RPC$

d)

$\Delta PRC$

22.

Use the congruency statement to answer the following: < F = ___

a)

< H

b)

< I

c)

< G

d)

not congruent to another angle

23.

∆ABC ≅ ∆XYZ, which is true?

a)

AB ≅ XY

b)

AB ≅ YX

c)

AB ≅ XZ

d)

BC ≅ CB

24.

∆ABC ≅ ∆LMN. Which statement is NOT true?

a)

LM ≅ AB

b)

∆CAB ≅ ∆NLM

c)

∠C ≅ ∠N

d)

BC ≅ ML

25.

a)

A

b)

B

c)

C

d)

D

26.

Complete the statement. ∠E ≅ __

a)

< A

b)

< B

c)

< C

d)

< D

27.

Which segment is congruent to EF?

a)

HG

b)

HF

c)

GF

d)

IE

28.

Complete the congruence statement.

a)

A

b)

B

c)

C

d)

D

29.

∆JIK ≅

a)

∆TRS

b)

∆RST

c)

∆STR

d)

∆TSR

30.

∆ISR ≅

a)

∆TRS

b)

∆RST

c)

∆STR

d)

∆TSR

31.

If ∆AIG ≅ ∆QOW, WQ ≅?

a)

AI

b)

GI

c)

AG

32.

Given the diagram, which of the following is true?

a)

∆XSF ≅ ∆XTG

b)

∆SXF ≅ ∆GXT

c)

∆FXS≅ ∆XGT

d)

∆FXS ≅ ∆GXT

33.

∠U = ≅

a)

∠F

b)

∠G

c)

∠E

34.

Complete the congruence statement.

a)

<G

b)

<F

c)

<E

35.

Complete the Congruence Statment.

a)

KJ

b)

JI

c)

KI

36.

Complete the statement.

a)

CE

b)

CD

c)

DE

d)

< E

37.

Complete the statement.

a)

$\Delta DEF$

b)

$\Delta FDE$

c)

$\Delta EDF$

d)

$\Delta FED$

38.

Complete the statement.

a)

$\Delta GEF$

b)

$\Delta FGE$

c)

$\Delta EFG$

d)

$\Delta EGF$

39.

Complete the congruence statement.

a)

< Z

b)

< R

c)

< P

d)

< Q

40.

Complete the congruence statement.

a)

TU

b)

XZ

c)

YZ

d)

YX

41.

If L is the midpoint of TJ, what must be true?

a)

TL=JT

b)

JL=TJ

c)

TL=LJ

d)

T is also the midpoint of JL

42.

If DA bisects IE, then

a)

ID=ED

b)

IA=EA

c)

<IDA=<EDA

d)

<IAD and <EAD are right angles

43.

If AD bisects <EDI, then

a)

<ADE=<IDA

b)

IA=AE

c)

ID=ED

d)

All of the above

44.

In this picture,

a)

<BCA=<DCE because they are vertical angles and vertical angles are always congruent to each other

b)

<C=<C because they are vertical angles and vertical angles are always congruent to each other

c)

<EDC=<ACB because they are vertical angles and vertical angles are always congruent to each other

d)

None of the above; we don't actually have vertical angles

45.

State if the two triangles are congruent. If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

46.

What is the "statement" for step 3 of the proof?

a)

HA=HA

b)

HA=AH

c)

MA=AM

d)

MA=MA

47.

What is always the 1st statement in reason column of a proof?

a)

Prove

b)

Given

c)

Reason

d)

Statement

48.

When using hypotenuse leg (HL) in a proof, you must first state ...

a)

CPCTC.

b)

there are right triangles.

c)

that vertical angles are congruent.

d)

the reflexive property.

49.

What is statement #1?

a)

b)

Given

c)

$\angle BCA\cong\angle DCE$

d)

50.

What is the reason for statement #1?

a)

Given

b)

$\overline{KM}\cong\overline{MK}$

c)

Definition of Congruent Segments

d)

Prove

51.

What is the reason for statement #2.

a)

Definition of midpoint

b)

Definition of congruent

c)

Definition of angle bisector

d)

Definition of segment bisector

52.

What is the reason for statement #3?

a)

SAS

b)

Prove

c)

SSA

d)

SSS

53.

What is the reason for statement #2?

a)

Definition of Segment Bisector

b)

Transitive Property

c)

Reflexive Property

d)

Definition of Midpoint

54.

Identify the missing statement or reason

a)

Reflexive Property

b)

Definition of Midpoint

c)

Given

d)

Vertical Angles Theorem

55.

Identify the missing statement or reason

a)

Given

b)

Vertical Angles Theorem

c)

Definition of Angle Bisector

d)

Alternate Interior Angles Theorem

56.

What statement and reason goes in the boxes labeled "1"?

a)

S: $\angle2\ \cong\ \angle1$

R: Alt Int $\angle$ Thm

b)

S: $\angle1\ \cong\ \angle4$

R: Alt Int $\angle$ Thm

c)

S: $\angle2\ \cong\ \angle4$

R: Alt Int $\angle$ Thm

d)

S: $\angle3\ \cong\ \angle1$

R: Alt Int $\angle$ Thm

57.

What statement and reason goes in the boxes labeled "2"?

a)

S: $\angle3\ \cong\ \angle4$

R: Alt Int $\angle$ Thm

b)

S: $\angle1\ \cong\ \angle4$

R: Alt Int $\angle$ Thm

c)

S: $\angle2\ \cong\ \angle4$

R: Alt Int $\angle$ Thm

d)

S: $\angle3\ \cong\ \angle1$

R: Alt Int $\angle$ Thm

58.

What statement and reason goes in the boxes labeled "3"?

a)

S: $\overline{ZX}\ \cong\ \overline{ZX}$

R: Reflexive PoC

b)

S: $\overline{ZW}\ \cong\ \overline{ZW}$

R: Reflexive PoC

c)

S: $\overline{YX}\ \cong\ \overline{YX}$

R: Reflexive PoC

d)

S: $\overline{ZY}\ \cong\ \overline{WX}$

R: Opposite sides are $\cong$

59.

What statement and reason goes in the boxes labeled "4"?

a)

S: $\Delta ZYX\ \cong\ \Delta XWZ$

R: ASA

b)

S: $\Delta ZYX\ \cong\ \Delta XWZ$

R: SAS

c)

S: $\Delta ZYX\ \cong\ \Delta XWZ$

R: AAS

d)

S: $\Delta ZYX\ \cong\ \Delta XWZ$

R: SSS

e)

S: $\Delta ZYX\ \cong\ \Delta XWZ$

R: HL

60.

What statement and reason goes in the boxes labeled "1"?

a)

S: $\overline{BO}\ \cong\ \overline{BO}$

R: Reflexive PoC

b)

S: $\overline{BH}\ \cong\ \overline{BC}$

R: Opp sides are $\cong$

c)

S: $\overline{OH}\ \cong\ \overline{OC}$

R: Opp sides are $\cong$

d)

S: $\overline{BO}\ \cong\ \overline{BO}$

R: Transitive PoC

61.

What statement and reason goes in the boxes labeled "2"?

a)

S: $\Delta BHO\ \cong\ \Delta BCO$

R: ASA

b)

S: $\Delta BHO\ \cong\ \Delta BCO$

R: SAS

c)

S: $\Delta BHO\cong\ \Delta BCO$

R: AAS

d)

S: $\Delta BHO\ \cong\ \Delta BCO$

R: SSS

e)

S: $\Delta BHO\cong\ \Delta BCO$

R: HL

62.

What statement and reason goes in the boxes labeled "1"?

a)

S: $\overline{DO}\ \cong\ \overline{HO}$

R: Def. of Segment Bisector

b)

S: $\overline{YT}\ \cong\ \overline{DH}$

R: Opp sides are $\cong$

c)

S: $\overline{OH}\ \cong\ \overline{OC}$

R: Given

d)

S:

$\overline{YO}\ \cong\ \overline{YO}$

R: Reflexive PoC

63.

What statement and reason goes in the boxes labeled "2"?

a)

S: $\overline{YO}\ \cong\ \overline{TO}$

R: Def. of Segment Bisector

b)

S: $\overline{YT}\ \cong\ \overline{DH}$

R: Opp sides are $\cong$

c)

S: $\overline{OH}\ \cong\ \overline{OC}$

R: Given

d)

S:

$\overline{YO}\ \cong\ \overline{YO}$

R: Reflexive PoC

64.

What statement and reason goes in the boxes labeled "3"?

a)

S: $\angle YOD\ \cong\ \angle HOT$

R: Vertical Angle Thm

b)

S: $\angle YOD\ \cong\ \angle HOT$

R: Alt Int Angle Thm

c)

S: $\angle YOD\ \cong\ \angle HOT$

R: Reflexive PoC

d)

S: $\angle O\ \cong\ \angle O$

R: Given

65.

What statement and reason goes in the boxes labeled "4"?

a)

S: $\Delta YOD\ \cong\ \Delta TOH$

R: ASA

b)

S: $\Delta YOD\ \cong\ \Delta TOH$

R: SAS

c)

S: $\Delta YOD\cong\ \Delta TOH$

R: AAS

d)

S: $\Delta YOD\ \cong\ \Delta TOH$

R: SSS

e)

S: $\Delta YOD\cong\ \Delta TOH$

R: HL

66.

What statement and reason goes in the boxes labeled "1"?

a)

S: $\angle TDP\ \&\ \angle ADP\ are\ 90\degree$ R: Def. of perpendicular

b)

S: $\angle TDP\ \&\ \angle ADP\ are\ 90\degree$ R: Given

c)

S: $\angle TDP\ \&\ \angle ADP\ are\ 180\degree$ R: Def. of perpendicular

d)

S: $\angle D\ \cong\ \angle D$ R: Reflexive PoC

67.

What statement and reason goes in the boxes labeled "2"?

a)

S: $\overline{PD}\ \cong\ \overline{PD}$ R: Reflexive PoC

b)

S: $\overline{TD}\ \cong\ \overline{AD}$ R: Def of Segment Bisector

c)

S: $\overline{TP}\ \cong\ \overline{AP}$ R: Opp. sides are $\cong$

d)

S: $\angle PTD\ \cong\ \angle PAD$ R: Alt. Int. Angle Thm.

68.

What statement and reason goes in the boxes labeled "3"?

a)

S: $\Delta TDP\ \cong\ \Delta ADP$

R: ASA

b)

S: $\Delta TDP\ \cong\ \Delta ADP$

R: SAS

c)

S: $\Delta TDP\cong\ \Delta ADP$

R: AAS

d)

S: $\Delta TDP\ \cong\ \Delta ADP$

R: SSS

e)

S: $\Delta TDP\cong\ \Delta ADP$

R: HL

69.

Fill in the proof with the labels below.

a)

AAS congruence theorem

b)

Definition of midpoint

c)

∠SEM

d)

CPCTC

e)

△SEM ≅ △KMR

f)

SAS congruence postulate

g)

SM

h)

∠SMR

i)

RM ≅ EM

j)

Alternate internal ∠’s are ≅

1

2

3

4

5

6

7

8

9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

70.

Identify the missing statement or reason

a)

Reflexive Property

b)

Definition of Midpoint

c)

Given

d)

Vertical Angles Theorem

71.

Identify the missing statement or reason

a)

Given

b)

Vertical Angles Theorem

c)

Definition of Angle Bisector

d)

Alternate Interior Angles Theorem

72.

Identify the missing statement or reason

a)

Definition of Angle Bisector

b)

Alternate Interior Angles Theorem

c)

Reflexive Property

d)

Definition of Midpoint

73.

What is the "statement" for step 3 of the proof?

a)

∡EDA≅∡DCB

b)

∡AED≅∡BEC

c)

DE=CE

d)

∡AED≅∡CED

74.

a)

A

b)

B

c)

C

d)

D

75.

a)

A

b)

B

c)

C

d)

D

76.

a)

A

b)

B

c)

C

d)

D

77.

What does CPCTC stand for?

a)

Corresponding Parts of Corresponding Triangles are Congruent

b)

Congruent Parts of Corresponding Triangles are Congruent

c)

Corresponding Parts of Congruent Triangles are Congruent

78.

What is the "statement" for step 2 of the proof?

a)

∆BAC≅∆DAC

b)

BC=DC

c)

∡B≅∡D

d)

∡BAC≅∡DAC

79.

What is the "reason" for step 3 of the proof?

a)

Proof

b)

Def. of Midpoint

c)

Reflexive Property

d)

Vertical angle Theorem

80.

When using hypotenuse leg (HL) in a proof, you must first state ...

a)

CPCTC.

b)

there are right triangles.

c)

that vertical angles are congruent.

d)

the reflexive property.

81.

What is the correct choice for Reason 4?

a)

⊿GHI ≅ ⊿JKL

b)

⊿GHI ≅ ⊿KLJ

c)

⊿GHI ≅ ⊿LJK

d)

⊿GHI ≅ ⊿LKJ

82.

What is the correct choice for Statement 5?

a)

SAS

b)

Definition of Congruence

c)

Prove

d)

CPCTC

83.

What is the correct choice for Reason 3?

a)

Vertical Angles are Congruent

b)

Definition of Congruence

c)

Given

d)

Reflexive Property

84.

What is the correct choice for Reason 4?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

85.

If L is the midpoint of TJ, what must be true?

a)

TL=JT

b)

JL=TJ

c)

TL=LJ

d)

T is also the midpoint of JL

86.

If DA bisects IE, then

a)

ID=ED

b)

IA=EA

c)

<IDA=<EDA

d)

<IAD and <EAD are right angles

87.

If AD bisects <EDI, then

a)

<ADE=<IDA

b)

IA=AE

c)

ID=ED

d)

All of the above

88.

If DA is perpendicular to IE, then we can immediately conclude that

a)

IA=AE

b)

<IAD = <DAE

c)

<IDA=<EDA

d)

<IAD and <DAE are right angles

89.

If DA bisects EI, then

a)

<IDA = <EDA

b)

AI=EA

c)

Both 1 and 2 are correct

d)

DI=ED

90.

If DA is the perpendicular bisector or EI, then

a)

<IAD and <DAE are right angles

b)

DI=DE

c)

EA=IA

d)

Both 1 and 3 are correct

91.

An angle bisector cuts an angle into two congruent _________

a)

Angles!

b)

Segments

c)

Mysteries

92.

A segment bisector cuts a segment into two congruent

a)

Segments!

b)

Angles

c)

Mysteries

93.

In this picture, we know for sure that

a)

<TEB=<ETS

b)

<BTE=<SET

c)

BE=ST

d)

Both 1 and 2 are correct

Triangle Congruence Theorems and Proofs Review

Total questions: 93

Worksheet time: 6hrs 15mins

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