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Chapter 4 Review - Congruent Triangles

Total questions: 60

Worksheet time: 14hrs 19mins

Name
Class
Date
1.
Complete the congruence statement.
a)
CRP
b)
PCR
c)
RPC
d)
PRC
2.

Use the congruency statement:

∆EFI ≅ ∆HGI

∠F = ___?

a)

∠H

b)

∠I

c)

∠G

d)

not congruent to another angle

3.

∆EHG≅∆KFC

Which is a true statement?

a)

EH‾≅FK‾\overline{EH}\cong\overline{FK}

b)

HG‾≅KF‾\overline{HG}\cong\overline{KF}

c)

EG‾≅KC‾\overline{EG}\cong\overline{KC}

d)

∠E≅∠C

4.

∆ABC ≅ ∆LMN

Which statement is NOT true?

a)

LM‾≅AB‾\overline{LM}\cong\overline{AB}

b)

∆CAB ≅ ∆NLM

c)

∠C≅∠N\angle C\cong\angle N

d)

BC≅ML‾BC\cong\overline{ML}

5.

State if the two triangles are congruent.

If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

6.

State if the two triangles are congruent.

If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

7.

State if the two triangles are congruent.

If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

8.

State if the two triangles are congruent.

If they are, state how you know.

a)

A

b)

B

c)

C

d)

D

9.

What additional information is required for the two triangles to be congruent by ASA?

a)

A

b)

B

c)

C

d)

D

10.

What additional information is required for the two triangles to be congruent by SAS?

a)

A

b)

B

c)

C

d)

D

11.

Pick the correct congruence statement.

a)

∆TUV ≅ ∆EUV

b)

∆VUT ≅ ∆UVE

c)

∆TUV ≅ ∆UEV

d)

∆UTV ≅ ∆EUV

12.

Which is NOT a test to prove triangles congruent?

a)

ASA

b)

SSS

c)

SSA

d)

SAS

13.

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

d)

Congruent Parts of Congruent Triangles are Congruent

14.

Fill in the missing reasons in the proof.

a)

Transitive Property, SAS(Side-Angle-Side)

b)

Reflexive Property, SAS(Side-Angle-Side)

c)

Reflexive Property, Vertical Angles Thm.

d)

Transitive Property, SSS(Side-Side-Side)

15.
What is the "statement" for step 2 of the proof?
a)
AD=AD
b)
AD=DA
c)
HD=DN
d)
HA = AN
16.

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

a)

∠EDA ≅ ∠DCB

b)

∠AED ≅ ∠BEC

c)

DE = CE

d)

∠AED ≅ ∠CED

17.

What are the two missing reasons in the proof?

a)

Transitive Property, SAS(Side-Angle-Side)

b)

Reflexive Property, SAS(Side-Angle-Side)

c)

Transitive Property, SSS(Side-Side-Side)

d)

Reflexive Property, SSS(Side-Side-Side)

18.

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

a)

∆BAC≅∆DAC

b)

BC=DC

c)

∠B ≅ ∠D

d)

∠BAC ≅ ∠DAC

19.
What is the "reason" for step 3 of the proof?
a)
Proof
b)
Def. of Midpoint
c)
Reflexive Property
d)
Vertical angle Theorem
20.

What would be the correct "given" statements for this diagram?

a)

T is the midpoint of segment BG ;

∠B ≅ ∠G

b)

∠B ≅ ∠G ;

∠A ≅ ∠W

c)

T is the midpoint of segment BG ;

∠A ≅ ∠W

d)

T is the midpoint of segment AW ;

∠A ≅ ∠W

21.

If C is the midpoint of AD and BE, what proves

∆ABC ≅ ∆EDC?

a)

SSS

b)

SAS

c)

ASA

d)

SSS

22.

What proves ∆ABC ≅ ∆MNO?

a)

SAS

b)

None

c)

SSS

d)

ASA

23.

What proves ∆ABC ≅ ∆CDA?

a)

SSS

b)

SAS

c)

none

d)

ASA

24.

What is the correct congruence statement?

ΔDEC ≅________?

a)

ΔAEB

b)

ΔEAB

c)

ΔBEA

d)

Not Congruent

25.

What proves ∆ABE ≅ ∆CDE?

a)

SSS

b)

SAS

c)

ASA

d)

Not Possible

26.

Use the congruency statement:

∆EFI ≅ ∆HGI

∠H = ___?

a)

∠G

b)

∠I

c)

∠E

d)

not congruent to another angle

27.

What proves ∆ABC ≅ ∆DEF?

a)

ASA

b)

AAS

c)

SSA

d)

Not congruent

28.

What is always the 1st "reason" of a proof?

a)

Prove

b)

Given

c)

Reason

d)

Statement

29.
∆JIK ≅
a)
∆TRS
b)
∆RST
c)
∆STR
d)
∆TSR
30.

Which pair(s) of shapes are congruent? (Select all congruent pairs)

a)
b)
c)
d)
31.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
32.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
33.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
34.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
35.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
AAS
c)
SAS
d)
Cannot be proven congruent
36.
Can the triangles be proven congruent?  If so, how?
a)
ASA
b)
Cannot be proven congruent
c)
SAS
d)
SSS
37.
What missing piece of information is needed to prove the triangles congruent using SAS?
a)
∠F≅∠Q
b)
∠G≅∠R
c)
∠H≅∠S
d)
FH = QS
38.
The figure is an example of a(n) ...
a)
angle bisector
b)
midsegment
c)
altitude
d)
median
39.

What is true about a perpendicular bisector of a triangle?

Select all that apply.

a)

It always starts from a vertex of the triangle.

b)

It is perpendicular to the side of a triangle.

c)

It passes through the midpoint of the side of the triangle.

d)

All of the above

40.
Which of the following describes a median of a triangle?
a)
A segment that is perpendicular to the side of a triangle at its midpoint.
b)
A segment with endpoints at the vertex and midpoint of the opposite side.
c)
A segment that connects two midpoints of two sides.
d)
A segment that connects the vertex and the opposite side at 90 degrees. 
41.

What is the blue line shown?

a)

median

b)

angle bisector

c)

perpendicular bisector

d)

altitude

42.

Which of the following special segments is shown?

a)

median

b)

angle bisector

c)

perpendicular bisector

d)

altitude

43.

If a point lies on the _________ of a segment, then the point is equidistant from the endpoints of the segment.

a)

perpendicular bisector

b)

median

c)

altitude

d)

angle bisector

44.

If a point is equidistant from the sides of an angle, then that point lies on the _________ of the angle.

a)

perpendicular bisector

b)

median

c)

altitude

d)

angle bisector

45.
Which angle is the vertex angle?
a)
<C
b)
<A
c)
<B
46.
a)
A
b)
B
c)
C
d)
D
47.
Find x
a)
90
b)
45
c)
22
d)
35
48.
Find x
a)
10
b)
32
c)
116
d)
16
49.
If two sides of a triangle are congruent, then the _________________ opposite those sides are congruent.
a)
sides
b)
vertices
c)
angles
d)
measures
50.
Fill in the missing pieces of the proof.
a)
Transitive Property, SAS(Side-Angle-Side)
b)
Reflexive Property, SAS(Side-Angle-Side)
c)
Reflexive Property, Vertical Angles Thm.
d)
Transitive Property, SSS(Side-Side-Side)
51.

What is the value of x?

a)

16

b)

17

c)

51

d)

78

52.
Use the picture to answer the question.
a)
30
b)
60
c)
15
d)
120
53.

What is this point of concurrency?

a)

Centroid

b)

Circumcenter

c)

Orthocenter

d)

Incenter

54.

What is this point of concurrency?

a)

Circumcenter

b)

Orthocenter

c)

Centroid

d)

Incenter

55.

What is this point of concurrency?

a)

Incenter

b)

Centroid

c)

Orthocenter

d)

Circumcenter

56.

What is this point of concurrency?

a)

Circumcenter

b)

Orthocenter

c)

Incenter

d)

Centroid

57.
If G is the centroid of triangle ABC and BE= 18. Find the length of BG.
a)
6
b)
12
c)
18
d)
Not Enough Information
58.

Point T is the incenter of the triangle. Find the length of RU to the nearest tenth.

a)

20.1

b)

12

c)

17.3

d)

18.4

59.

Point W is the centroid of the triangle. Solve for x.

a)

30

b)

7

c)

15

d)

2

60.
What is point J called?
a)
centroid
b)
incenter
c)
circumcenter
d)
orthocenter

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