Free Printable Proving Triangles Congruent

1.

What is the reason these triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

2.

What is the reason these triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

3.

What is the reason these triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

4.

What is the reason these triangles are congruent?

a)

SSS

b)

SAS

c)

ASA

d)

AAS

5.

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

a)

SSS

b)

SAS

c)

ASA

d)

Not Possible

6.

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

a)

SSS

b)

ASA

c)

AAS

d)

Not Possible

7.

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

a)

SSS

b)

SAS

c)

AAS

d)

Not Possible

8.

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

a)

SSS

b)

SAS

c)

ASA

d)

AAS

9.

State if the triangles are congruent and why.

a)

Not congruent

b)

SAS

c)

ASA

d)

HL

10.

State if the triangles are congruent and why.

a)

AAS

b)

SAS

c)

ASA

d)

Not congruent

11.

State if the triangles are congruent and why.

a)

AAS

b)

ASA

c)

Not congruent

d)

SSS

12.

State if the triangles are congruent and why.

a)

ASA

b)

AAS

c)

SAS

d)

Not congruent

13.

State if the triangles are congruent and why.

a)

HL

b)

SAS

c)

Not congruent

d)

AAS

14.

∆ABC≅∆XYZ

which is true?

a)

AB≅XY

b)

AB≅YZ

c)

AB≅XZ

d)

BC≅AB

15.

∆EHG≅∆KFC

Which is a true statement?

a)

EH≅FC

b)

HG≅KF

c)

EG≅KC

d)

∠E≅∠C

16.

Name the corresponding angle or side.

a)

A

b)

B

c)

C

d)

D

17.

Name the corresponding angle or side.

a)

A

b)

B

c)

C

d)

D

18.

Which is a correct congruence statement.

a)

A

b)

B

c)

C

d)

D

19.

What does CPCTC stand for?

a)

Congruent parts of congruent triangles are congruent

b)

Corresponding parts of congruent triangles are congruent

c)

Corresponding parts of corresponding triangles are corresponding

d)

Corresponding parts of congruent triangles are Canadian.

20.

Given the two triangles, which congruence statement is NOT true?

a)

$AB\ \cong\ DF$

b)

$DE\ \cong\ AC$

c)

$\Delta\ ABC\ \cong\ \Delta DFE$

d)

$\Delta ABC\ \cong\Delta\ DEF$

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

∠A ≅∠?

a)

∠B

b)

∠E

c)

∠D

d)

∠F

27.

The hypotenuse of a triangle is...

a)

Invisible

b)

A myth

c)

The side opposite the right angle in a right triangle

28.

Is Angle-Angle-Angle (AAA), a valid rule for proving triangles congruent?

a)

No

b)

Sometimes

c)

Yes

d)

N/A

29.

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

a)

A)

b)

B)

c)

C)

d)

D)

30.

What does CPCTC stand for?

a)

Corresponding Parts of Congruent Triangles are Congruent

b)

Congruent Parts of Congruent Triangles are Corresponding

c)

Corresponding Parts of Canadian Triangles are Cool

d)

Congruent Parts of Corresponding Parts are Corresponding

31.

Which of the following is NOT a valid reason to prove congruent triangles?

a)

SSA

b)

ASA

c)

SAS

d)

SSS

32.

Remember order matters. Which of the following is true?

a)

∆FGH ≅ ∆VHW

b)

∆HFG ≅ ∆HWV

c)

∆HGF ≅ ∆VHW

d)

∆FGH ≅ ∆VWH

33.

These two triangles are congruent. If ∠C is 40^o find the measure of ∠F.

a)

40^o

b)

50^o

c)

90^o

d)

45^o

34.

Which segment is the base?

a)

Segment AB

b)

Segment BC

c)

Segment AC

35.

Which segments are the legs?

a)

Segment AB

b)

Segment BC

c)

Segment AC

36.

Find the value of y.

a)

5

b)

10

c)

15

d)

20

37.

Find the value of z.

a)

5

b)

10

c)

15

d)

20

38.

Find the value of y?

a)

16

b)

12

c)

4

d)

8

39.

Find the value of x

a)

18

b)

180

c)

25

d)

30

40.

Find the value of x

a)

10

b)

52

c)

9

d)

7

41.

a)

56

b)

62

c)

68

d)

112

42.

Find the value of x. (Hint: What type of triangle is this?)

a)

4

b)

1

c)

-4

d)

10

43.

Triangle KLM is equilateral with KM = x + 2, LM = 12 – x, and KL = 4x – 13.

Find the value of x.

(Hint: draw a picture)

a)

2

b)

3

c)

4

d)

5

44.

Triangle DEF is isosceles, angle D is the vertex angle, DE = x + 7, DF = 3x – 1, and EF = 2x + 5.

Find the value of x.

a)

2

b)

4

c)

6

d)

8

45.

Find x.

a)

10

b)

$10\sqrt{3}$

c)

$10\sqrt{2}$

d)

20

46.

Find a.

a)

12

b)

24

c)

$24\sqrt{3}$

d)

16

47.

Find a.

a)

9

b)

$9\sqrt{3}$

c)

$\frac{9}{2}$

d)

$6\sqrt{3}$

48.

a)

22

b)

22√2

c)

44

d)

44√3

49.

a)

12

b)

6

c)

5

d)

18

50.

From ∠C, what side is AB?

a)

Adjacent

b)

Hypotenuse

c)

Opposite

51.

Find the ratio for sinA. (Reduce the fraction)

a)

36/27

b)

4/5

c)

36/45

d)

3/5

52.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

53.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

54.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

55.

a)

A

b)

B

c)

C

d)

D

56.

Name this triangle by its sides

a)

scalene

b)

isosceles

c)

equilateral

d)

acute

57.

Name this triangle by its sides.

a)

scalene

b)

isosceles

c)

equilateral

d)

obtuse

58.

Name this triangle by its angle and sides.

a)

acute, scalene

b)

obtuse scalene

c)

right, scalene

d)

right, isosceles

59.

Name this triangle by its angles and sides.

a)

acute, scalene

b)

acute, isosceles

c)

obtuse, equilateral

d)

equiangular, equilateral

60.

Name this triangle by its angles and sides.

a)

obtuse, isosceles

b)

acute isosceles

c)

right, scalene

d)

acute, equilateral

61.

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______.

a)

45°

b)

90°

c)

180°

d)

360°

62.

The dotted line represents a ?...

a)

median

b)

centroid

c)

midsegment

d)

midpoint

63.

The figure is an example of a(n) ...

a)

angle bisector

b)

perpendicular bisector

c)

median

d)

midsegment

64.

The figure is an example of a(n) ...

a)

altitude

b)

perpendicular bisector

c)

midsegment

d)

angle bisector

65.

Which of the following segments represents an altitude?

a)

BX

b)

AZ

c)

AC

d)

BZ

66.

The smallest angle would be located where in a triangle?

a)

Across from the smallest side.

b)

Across from the largest side

c)

Cannot tell

67.

Where would the largest side of a triangle be located?

a)

Across from the largest angle.

b)

Across from the smallest angle.

c)

Next to the smallest side.

d)

Across the smallest side.

68.

Name the angles from SMALLEST to LARGEST

a)

Q, R, P

b)

P, Q, R

c)

R, P, Q

d)

R, Q, P

69.

Find the largest angle in Δ PRQ

a)

∠R

b)

∠P

c)

∠Q

d)

∠S

70.

Given the two parallel lines cut by a transversal.

What is the vertical angle to angle 4?

a)

Angle 2

b)

Angle 6

c)

Angle 8

d)

Angle 7

71.

Given the following two parallel lines cut by a transversal.

Which pair of angles represents corresponding angles?

a)

$\angle1$ and $\angle6$

b)

$\angle6$ and $\angle5$

c)

$\angle7$ and $\angle8$

d)

$\angle4$ and $\angle8$

72.

Given the following two parallel lines cut by a transversal.

Which pair of angles represents alternate interior angles?

a)

$\angle3$ and $\angle8$

b)

$\angle7$ and $\angle2$

c)

$\angle7$ and $\angle8$

d)

$\angle4$ and $\angle8$

73.

Given the two parallel lines cut by a transversal,

What is the measure of $\angle5$ ?

(a)

74.

a)

15

b)

16

c)

18

d)

19

75.

Find the m∠1

a)

67

b)

113

c)

180

d)

23

76.

The supplement of an angle is 65 °. What is the measure of the angle?

a)

25°

b)

15°

c)

115°

d)

35°

77.

Angle 4 = x + 15

Angle 2 = 3x - 5

What is the value of x?

a)

5

b)

10

c)

25

d)

x + 15

78.

Solve for x.

a)

1

b)

2

c)

3

d)

4

79.

Set up an equation to find x.

a)

42 + 8x = 2 + 12x

b)

2 + 12x + 42 = 8x

c)

42 + 8x + 2 + 12x = 180

d)

42 + 8x = 180

80.

Do the following side lengths form a triangle?
2 inches, 2 inches, 4 inches

a)

Yes

b)

No

81.

Can the following side measures form a triangle?
4 cm, 7 cm, 10 cm

a)

Yes

b)

No

82.

What is the range of values of x for a triangle's third side given side measures of 8 and 15?

a)

between 8 and 15

b)

between 7 and 23

c)

less than 7, greater than 23

83.

What is the range of values of x for a triangle's third side given side measures of 4 and 12?

a)

between 8 and 16

b)

less than 4, greater than 12

c)

between 4 and 12

84.

Two sides of a triangle have the following measures. Find the range of possible measure for the third side.
$10,6$

a)

$4<x<16$

b)

$5<x<15$

c)

$6<x<15$

d)

$4<x<14$

85.

Two sides of a triangle have the following measures. Find the range of possible measure for the third side.
$8,9$

a)

$1<x<17$

b)

$1<x<13$

c)

$1<x<15$

d)

$2<x<15$

Proving Triangles Congruent

Total questions: 85

Worksheet time: 3hrs 10mins

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