Free Printable Geometry: Chapter 4 (Triangle Congruence)

1.

Are these two triangles congruent? If so, state the theorem.

a)

No, not enough info.

b)

Yes - SSS

c)

Yes - SAS

d)

Yes - ASA

2.

Are these two triangles congruent? If so, state the theorem.

a)

No, not enough info.

b)

Yes - AAA

c)

Yes - ASA

d)

Yes - AAS

3.

Are these two triangles congruent? If so, state the theorem.

a)

No, not enough info.

b)

Yes - AAA

c)

Yes - SSS

d)

Yes - HL

4.

Are these two triangles congruent? If so, state the theorem.

a)

No, not enough info.

b)

Yes - AAS

c)

Yes - HL

d)

Yes - SSS

5.

Are these two triangles congruent? If so, state the theorem.

a)

No, not enough info.

b)

Yes - SAS

c)

Yes - HL

d)

Yes - SSA

6.

Are these two triangles congruent? If so, state the theorem.

a)

No, not enough info.

b)

Yes - AAS

c)

Yes - AAA

d)

Yes - ASA

7.

AB = 7 and AD = 8 and DB = 10 If the triangles are congruent, how long is CB?

a)

7

b)

8

c)

10

d)

The triangles are not congruent

8.

These triangles are congruent. If ∠E is 45^o and ∠B is 55^o what is the measure of ∠C?

a)

45^o

b)

55^o

c)

80^o

d)

100^o

9.

Name the corresponding angle or side.

a)

A

b)

B

c)

C

d)

D

10.

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

a)

AAS

b)

SSS

c)

SAS

d)

SSA

11.

Name the postulate, if possible, that makes the triangles congruent.

a)

SAS

b)

ASA

c)

AAS

d)

Not Possible

12.

How are the triangles congruent?

a)

HL

b)

SSS

c)

SAS

d)

AAS

13.

$\Delta BIG\cong\Delta LAD$ , which side is congruent to $\overline{BG}$ ?

a)

$\overline{BI}$

b)

$\overline{LA}$

c)

$\overline{AD}$

d)

$\overline{LD}$

14.

$\Delta BIG\cong\Delta LAD$ , which angle is congruent to $\angle B$ ?

a)

$\angle G$

b)

$\angle L$

c)

$\angle A$

d)

$\angle D$

15.

If $\Delta GAM\cong\Delta ERS$ , what angle is congruent to $\angle RES$ ?

a)

$\angle GAM$

b)

$\angle AGM$

c)

$\angle GMA$

d)

$\angle MAG$

16.

$\Delta GAM\cong\Delta ERS$ , $\overline{GA}=11$ , $\overline{GM}=8$ , and $\overline{AM}=7$ . What is the length of $\overline{ER}$ ?

a)

7

b)

8

c)

11

d)

26

17.

Given that $\Delta STA\cong\Delta BLE$ . If $m\angle S=97\degree$ and $m\angle T=43\degree$ ? What is the measure of angle L?

a)

$40\degree$

b)

$43\degree$

c)

$90\degree$

d)

$97\degree$

18.

What postulate or theorem proves that $\Delta ALE\cong\Delta RTE$ ?

a)

AAS Theorem

b)

ASA Postulate

c)

SAS Postulate

d)

SSS Postulate

19.

What triangle is congruent to $\Delta ALT$ ?

a)

$\Delta LRT$

b)

$\Delta RTL$

c)

$\Delta TLR$

d)

$\Delta TEL$

20.

What postulate or theorem proves that $\Delta ALT\cong\Delta RTL$ ?

a)

AAS Theorem

b)

ASA Postulate

c)

SAS Postulate

d)

SSS Postulate

21.

What triangle congruence postulate or theorem justifies the congruency of $\Delta RTO\ and\ \Delta BSO$ ?

a)

AAS Theorem

b)

ASA Postulate

c)

SAS Postulate

d)

SSS Postulate

22.

What triangle congruence postulate or theorem justifies the congruency of $\Delta IEL\cong\Delta EIF$ ?

a)

AAS Theorem

b)

ASA Postulate

c)

SAS Postulate

d)

SSS Postulate

23.

What parts of the triangles must be marked so that the triangles are congruent via SAS Postulate?

a)

$\angle B\ and\ \angle P$

b)

$\angle A\ and\ \angle E$

c)

$\angle G\ and\ \angle N$

24.

What parts of the triangles must be marked so that $\Delta HOE\ and\ \Delta POE$ are congruent via AAS Theorem?

a)

$\angle H\ and\ \angle P$

b)

$\angle HEO\ and\ \angle PEO$

c)

$\overline{HO}\ and\ \overline{PO}$

d)

$\overline{HE}\ and\ \overline{PE}$

25.

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

a)

SSS

b)

SAS

c)

ASA

d)

NONE

26.

a)

Congruent by HL

b)

Congruent by SAS

c)

Congruent by SSS

d)

Not Necessarily Congruent

27.

a)

Congruent by ASA

b)

Congruent by SAS

c)

Congruent by SSS

d)

Not Necessarily Congruent

28.

Which is not a postulate to prove triangle congruence?

a)

AAA

b)

ASA

c)

SSS

d)

SAS

29.

If ∆LMK ≅ ∆LMT, then ∠K ≅ ____

a)

$L$

b)

$\angle L$

c)

$\angle T$

d)

T

30.

How are the triangles congruent?

a)

HL

b)

SSS

c)

SAS

d)

AAS

31.

Given

\Delta ABC\ \cong\Delta DEF\

\angle A\ \cong\ ?

a)

$\angle D$

b)

$\angle E$

c)

$\angle F$

d)

$\angle C$

32.

Given

$\Delta ABC\ \cong\Delta DEF\$ $\overline{BC}\ \cong\ ?$

a)

$\overline{DE}$

b)

$\overline{EF}$

c)

$\overline{DF}$

d)

$\overline{FD}$

33.

Solve for the value of X.

X= (a)

34.

a)

72

b)

67

c)

65

d)

54

35.

What is the measure of ∠S?

a)

not enough information

b)

30

c)

60

d)

180

36.

When can we use the HL Congruence Theorem?

a)

Right Triangles

b)

Isosceles Triangles

c)

When we have a reflexive side

d)

SSA

37.

How are the triangles congruent?

a)

SAS

b)

ASA

c)

HL

d)

SSS

38.

What additional information is required to prove the two triangles are congruent by HL?

a)

A)

b)

B)

c)

C)

d)

D)

39.

Can the HL Congruence Theorem be used to prove the triangles congruent? If so, write a congruence statement.

a)

Yes, △ABC≅△NLM

b)

Yes, △CBA≅△NLM

c)

Yes, △CBA≅△MLN

d)

No

40.

a)

s = 33, t = 8

b)

s = 11, t = 4

c)

s = 39, t = 10

d)

s = 13, t = 5

41.

a)

x = 9, y = 30

b)

x = 5, y = 20

c)

x = 4.5, y = 10

d)

x = 2.5, y = 6.66

42.

Identify any common angles or sides

a)

$\overline{JK}$

b)

$\angle MJK$

c)

$\overline{LK}$

d)

$\angle MKJ$

43.

Identify common angles or sides

a)

$\angle E$

b)

$\angle D$

c)

$\angle F$

d)

$\angle DGF$

44.

The red (ΔKNM) and blue (ΔPLM) triangles are congruent. Identify a common side or angle.

a)

$\angle M$

b)

$\angle P$

c)

$\angle K$

d)

$\angle MLP$

45.

What is statement #4?

a)

$\angle B\cong\angle C$

b)

$\angle BDX\cong\angle CDY$

c)

$\angle AXC\cong\angle AYB$

46.

Step 6, complete the congruence statement and give the reason.

a)

CXA, HL

b)

CAX, HL

c)

CAX, ASA

d)

CXA, ASA

47.

What is the reason for Step 8?

a)

ASA

b)

SAS

c)

SSS

d)

AAS

48.

Is there enough information to conclude that the two triangles are congruent? If so, what is the correct congruence statement?

a)

Yes, $\Delta CAB\cong\Delta DAC$

b)

Yes, $\Delta ACB\cong\Delta ADC$

c)

Yes, $\Delta ABC\cong\Delta ADC$

d)

No, the triangles cannot be proven congruent

49.

What is the length of side JK?

a)

12

b)

30

c)

33

d)

3

50.

If ∆JKL is isosceles, what is m∠JKL?

a)

37°

b)

74°

c)

106°

d)

143°

51.

Find x

a)

90

b)

45

c)

22

d)

35

52.

Find the value of x.

a)

1

b)

4

c)

5

d)

8

53.

Find x

a)

60

b)

48

c)

30

d)

28

54.

Find the value of y.

a)

y=2

b)

y=18

c)

y=8.22

d)

y=9.33

55.

Solve for x.

a)

7

b)

9

c)

10

d)

-11

56.

What is the value of x?

a)

51

b)

49

c)

78

57.

Look at the sides of this triangle. What type of triangle is this?

a)

Equilateral

b)

Isosceles

c)

Scalene

d)

Obtuse

58.

What is the value of the missing angle?

a)

61

b)

50

c)

60

d)

69

59.

Which angle is the vertex angle?

a)

<C

b)

<A

c)

<B

60.

Find the measure of the indicated angle.

a)

34

b)

46

c)

62

d)

36

61.

Describe the transformation in the image.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

62.

Identify the transformation from ABC to A'B'C'.

a)

90^o clockwise rotation

b)

90^o counter clockwise rotation

c)

Reflection across the y-axis

d)

Reflection across the x-axis

63.

Are these triangles congruent?

a)

Yes, by ASA

b)

Yes, by SAS

c)

Yes, by AAS

d)

No, this is the SSA one!!

64.

Which is NOT a test to prove triangles congruent?

a)

SAA

b)

SSS

c)

SSA

d)

SAS

65.

What is the correct values for x and y?

a)

x = 40, y = 35

b)

x = 35, y = 40

c)

x = 12, y = 30

d)

x = 30, y = 15

66.

If the red triangle is rotated 180 degrees, then reflected over y=2 what is the final image?

a)

Green Triangle

b)

Blue Triangle

c)

Orange Triangle

d)

Red Triangle

67.

Under what composition of transformations does triangle ABC map onto triangle A''B''C''

a)

Reflection over x-axis, then Rotation of 90 Degrees.

b)

Rotation of -90 Degrees, then Reflection over y-axis

c)

Reflection over y-axis, then Rotation of -90 Degrees

d)

Rotation of 90 Degrees, then Reflection over x-axis

68.

Identify the correct picture which represents a 90^o clockwise rotation about the origin.

a)

b)

c)

d)

69.

What does it mean for two triangles to be congruent?

a)

Two triangles are congruent if they have the same shape but different sizes.

b)

Two triangles are congruent if they have the same size but different shapes.

c)

Two triangles are congruent if they have different shapes and sizes.

d)

Two triangles are congruent if they have the same shape and size.

70.

If two triangles are congruent, what can you say about their corresponding angles?

a)

Their corresponding angles are equal.

b)

Their corresponding angles are supplementary.

c)

Their corresponding angles are complementary.

d)

Their corresponding angles are not equal.

71.

What are the five ways to prove triangles congruent?

a)

SSS, ASA, AAS, SAS, HL

b)

SSS, SSA, HL, AAS, SAS

c)

SAS, SSA, HL, AAS, SSS

d)

HL, SAS, SSA, SSS, ASA

Geometry: Chapter 4 (Triangle Congruence)

Total questions: 71

Worksheet time: 7hrs 8mins

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