Free Printable Triangle Angle and Length Theorems Review

1.

Classify the triangle by angle.

a)

right

b)

acute

c)

obtuse

d)

equiangular

2.

Classify the triangle's sides.

a)

scalene

b)

obtuse

c)

equilateral

d)

isosceles

3.

Classify the triangle by sides.

a)

isosceles

b)

equilateral

c)

scalene

d)

obtuse

4.

Classify the triangle by angle.

a)

acute

b)

obtuse

c)

equiangular

d)

right

5.

Classify triangle CDF by angle and side.

a)

acute scalene

b)

obtuse scalene

c)

obtuse isosceles

d)

tooty fruity

6.

Classify the triangle EFD.

a)

equiangular equilateral triangle

b)

acute isosceles triangle

c)

equiangular scalene

7.

Classify triangle ABE.

a)

right scalene triangle

b)

right isosceles triangle

c)

right equiangular triangle

8.

Classify the triangle by angle and side.

a)

equiangular equilateral triangle

b)

acute equilateral angle

c)

acute isosceles triangle

d)

equiangular isosceles

9.

Classify the triangle by angle and side.

a)

right isosceles triangle

b)

right scalene triangle

c)

right equilateral triangle

d)

acute isosceles triangle

10.

Classify the triangle by angle and side.

a)

Right Scalene Triangle

b)

Right Isosceles Triangle

c)

Right Equilateral Trianbgle

11.

Match the following triangle classifications based on their sides.

a)

Scalene

1.

No congruent sides

b)

Isosceles

2.

Two congruent sides

c)

Equilateral

3.

Three congruent sides

12.

Match the following triangles with their angle classification.

a)

1.

Right Triangle

b)

2.

Acute Triangle

c)

3.

Obtuse Triangle

13.

Match the following triangles with their side classification.

a)

1.

Equilateral Triangle

b)

2.

Scalene Triangle

c)

3.

Isosceles Triangle

14.

How would you classify this triangle by it's sides and angles?

a)

Isosceles Acute

b)

Scalene Right

c)

Scalene Obtuse

d)

Isosceles Obtuse

e)

Isosceles Right

15.

How would you classify this triangle by it's sides and angles?

a)

Scalene Acute

b)

Equilateral

c)

Scalene Obtuse

d)

Isosceles Acute

e)

Isosceles Obtuse

16.

What is the best classification for this triangle?

a)

Isosceles Acute

b)

Scalene Acute

c)

Isosceles Obtuse

d)

Equilateral

e)

Scalene Obtuse

17.

What do the interior angles in a triangle have a sum of?

a)

180

b)

90

c)

360

d)

270

18.

Side Classification: (a)

Angle Classification: (b)

Choose from the below words

Scalene

Right

Isosceles

Acute

Obtuse

Equilateral

19.

Side Classification: (a)

Angle Classification: (b)

Choose from the below words

Isosceles

Acute

Right

Obtuse

Equilateral

Scalene

20.

Side Classification: (a)

Angle Classification: (b)

Choose from the below words

isosceles

right

scalene

obtuse

equilateral

acute

21.

Match the following triangles with their side and angle classification.

a)

1.

Equilateral

b)

2.

Scalene Obtuse

c)

3.

Scalene Right

d)

4.

Isosceles Acute

22.

Classify the triangle by angles and sides.

a)

Equiangular Equilateral

b)

Right Isosceles

c)

Right Scalene

d)

Acute Isosceles

23.

Classify the triangle by angles and sides.

a)

Obtuse Scalene

b)

Obtuse Isosceles

c)

Right Scalene

d)

Acute Isosceles

24.

Classify the triangle by angles and sides.

a)

Obtuse Scalene

b)

Obtuse Isosceles

c)

Acute Isosceles

d)

Equiangular Scalene

25.

Classify the triangle by angles and sides.

a)

Right Scalene

b)

Right Isosceles

c)

Acute Isosceles

d)

Right Obtuse

26.

Distance represents...

a)

the steepness of a line/segment.

b)

length of a segment.

c)

the half way point of a segment.

27.

How many times should you use the distance formula to determine if a triangle is scalene, isosceles or equilateral?

a)

1

b)

2

c)

3

d)

4

28.

What formula is shown?

a)

slope

b)

distance

c)

midpoint

d)

Pythagorean Theorm

29.

Find the distance between points B and C to the nearest tenth.

a)

8.4

b)

6.9

c)

8

d)

7.1

30.

Points G, H, and I are plotted on the coordinate grid. How many units are between points G and H?

a)

9 units

b)

14 units

c)

13 units

d)

12 units

31.

Use the distance formula to classify the following triangle

A (1 , 0) B (3 , 1) C (4 , 5)

a)

Equilateral

b)

Scalene

c)

Isnosceles

d)

Right angled

32.

How do we prove a triangle is a right triangle?

a)

Prove all sides are different lenghts

b)

Show that the three sides satisfy the pythagorean theorem

c)

Show that opposite angles are congruent

d)

Show that two sides are congruent

33.

Given the vertices of triangle ELV, Leo must prove that it is an isoceles right triangle. Which of the following calculations must Leo do?

a)

Use the Distance Formula and the Pythagorean Theorem to show that the Pythagorean Theorem is true.

b)

Use the Midpoint Formula to show that the Pythagorean Theorem is true.

c)

Use the Midpoint Formula to show that the slopes are perpendicular.

d)

Use the Slope Formula to show that two side lengths are equal.

34.

To prove that triangle ABC is equilateral, Barry decided to show that all side lengths are equal. To do so, which calculation must Barry perform?

a)

Find the midpoint of each segment, using the midpoint formula.

b)

Find the length of each segment, using the distance formula.

c)

Find the altitude, using the distance formula.

d)

Find the length of the hypotenuse, using the Pythagorean Theorem.

35.

Which of these triangles is a right triangle?

a)

6, 8, 10

b)

3, 7, 8

36.

Which of these triangles is a right triangle?

a)

7, 8, 10

b)

42, 56, 70

37.

Can the following 3 numbers be side measures of a triangle

11, 12, 9

a)

Yes

b)

No

38.

Can the following 3 numbers be side measures of a triangle

5, 8, 4

a)

Yes

b)

No

39.

Can the following 3 numbers be side measures of a triangle

8, 2, 8

a)

Yes

b)

No

40.

Can the following 3 numbers be side measures of a triangle

3, 6, 2

a)

Yes

b)

No

41.

Find the measure of the angle indicated.

a)

139°

b)

66°

c)

138°

d)

116°

42.

Find the measure of the missing angle.

a)

90^o

b)

10⁰

c)

130^o

d)

50^o

43.

Find the measure of the indicated angle.

a)

26

b)

36

c)

85

d)

144

44.

Find the measure of the indicated angle.

a)

95

b)

85

c)

35

d)

45

45.

What is the measure of angle b

a)

146

b)

34

c)

36

d)

136

46.

If 2 of the angles of a triangle are 30 and 70 degrees, the third angle measures...

a)

80

b)

100

c)

60

d)

90

47.

Find the measure of angle A.

a)

44^o

b)

96^o

c)

-14^o

d)

63^o

48.

Solve for x.

a)

71

b)

-3

c)

35

d)

-19

49.

Find the measure of angle A.

a)

75^o

b)

60^o

c)

30^o

d)

38^o

50.

A student is trying to construct triangles using four different sets of angles. The angles in each set are given below. Which set will form a triangle?

a)

45°, 65°, 70°

b)

150°, 110°, 100°

c)

50°, 50°, 50°

d)

90°, 90°, 90°

51.

Which of the following terms best describes Angle d?

a)

Remote interior angle

b)

Corresponding angle

c)

Exterior angle

d)

Interior angle

52.

Find the indicated angle. (What is ?)

a)

91°

b)

81°

c)

89°

d)

109°

53.

What is the measure of angle b?

a)

36^o

b)

56^o

c)

63^o

d)

117^o

54.

Find the indicated angle measure. (What is ?)

a)

51°

b)

37°

c)

167°

d)

41°

55.

Solve for x

a)

49

b)

58

c)

70

d)

94

56.

Solve for x

a)

70

b)

23

c)

120

d)

130

57.

Solve for x

a)

60

b)

120

c)

40

d)

65

58.

Which of the following angles can you add together to equal angle d?

a)

Angle a and Angle b

b)

Angle b and Angle c

c)

Angle a and Angle c

d)

Angle a and Angle b and Angle c

59.

Solve for x.

a)

13

b)

8

c)

11

d)

4

60.

Solve for x.

a)

34

b)

9

c)

109

d)

7

61.

How do you find the missing angle?

a)

124 + 77

b)

2(77)

c)

180 - 77

d)

124 - 77

62.

Find the value of x by using the exterior angle theorem.

a)

A

b)

B

c)

C

d)

D

63.

Find the value of x by using the exterior angle theorem.

a)

A

b)

B

c)

C

d)

D

64.

Find the measure of the indicated angle.

a)

145

b)

113

c)

102

d)

78

65.

Find the measure of each angle indicated.

a)

50

b)

85

c)

45

d)

49

66.

Solve for the unknown angle.

a)

49

b)

58

c)

70

d)

94

67.

Solve for x.

a)

6

b)

8

c)

15

d)

13

68.

Which of the following terms best describes Angle a?

a)

Remote interior angle

b)

Corresponding angle

c)

Exterior angle

d)

Obtuse angle

69.

Find the measure of the indicated angle.

a)

145 degrees

b)

24 degrees

c)

20 degrees

d)

21 degrees

70.

Find the measure of the indicated angle.

a)

87 degrees

b)

82 degrees

c)

83 degrees

d)

72 degrees

71.

Solve for x.

a)

5

b)

12

c)

-7

d)

-6

72.

What is the measure of ∠S?

a)

not enough information

b)

$30\degree$

c)

$60\degree$

d)

$90\degree$

73.

What is the measure of BC?

a)

12

b)

6

c)

not enough information

d)

10

74.

What is the measure of ∠A?

a)

46

b)

134

c)

90

d)

88

75.

Find the measure of $\angle M$

a)

$54\degree$

b)

$27\degree$

c)

$26\degree$

d)

$36\degree$

76.

What angles are congruent?

a)

$\angle P\cong\angle V$

b)

$\angle K\cong\angle P$

c)

$\angle V\cong\angle K$

d)

$\angle P\cong\angle K\cong\angle V$

77.

What sides are congruent?

a)

$\overline{AM}\cong\overline{KM}$

b)

$\overline{KA}\cong\overline{MK}$

c)

$\overline{KA}\cong\overline{AM}$

d)

$\overline{MA}\cong\overline{KA}\cong\overline{MK}$

78.

Solve for x.

a)

55

b)

52

c)

65

d)

41

79.

Solve for x.

a)

30

b)

34

c)

36

d)

26

80.

Determine x

a)

93

b)

71

c)

81

d)

55

81.

What is the equation you would use to find x?

a)

3x = x

b)

3x + x = 180

c)

3x + 3x + x = 180

d)

3x + x + x = 180

82.

What is the equation you would use to find y?

a)

7y = 4y - 15

b)

7y + 4y - 15 = 180

c)

7y + 4y - 15 + 4y - 15 = 180

d)

7y + 7y + 4y - 15 = 180

83.

What is the equation you would use to find x?

a)

4x + 1 = 5x - 4

b)

4x + 1 + 5x - 4 = 180

c)

4x + 1 + 4x + 1 + 5x - 4 = 180

d)

4x + 1 + 5x - 4 + 5x - 4 = 180

84.

x = (a)

85.

x = (a)

86.

x = (a)

87.

x = (a)

88.

a)

60

b)

120

c)

15

d)

30

89.

Find x.

a)

180

b)

57

c)

61.5

d)

32.7

90.

Solve for X

a)

11

b)

23

c)

15

d)

5

91.

For the equilateral triangle solve for x

a)

9

b)

11

c)

-9

d)

129

92.

What is the value of x?

a)

20

b)

60

c)

15

d)

40

93.

What is the value of y?

a)

7

b)

4

c)

6

d)

14

94.

Find x

a)

3

b)

4

c)

2

d)

10

95.

Solve for X.

a)

4

b)

8

c)

12

d)

60

96.

Solve for Y.

a)

4

b)

8

c)

12

d)

60

97.

Solve for y. (Take your time and figure it out!)

a)

5

b)

4

c)

20

d)

12

98.

Solve for x. (Take your time and figure it out!)

a)

60^o

b)

120^o

c)

30^o

d)

50^o

99.

Find x

a)

3

b)

4

c)

2

d)

10

100.

Solve for x.

a)

72^o

b)

144^o

c)

46^o

d)

36^o

101.

Solve for x.

a)

130^o

b)

50^o

c)

25^o

d)

70^o

102.

Find x

a)

10

b)

32

c)

116

d)

16

103.

Find x

a)

90

b)

45

c)

22

d)

35

104.

What is the equation you would use to find x?

a)

4x + 1 = 5x - 4

b)

4x + 1 + 5x - 4 = 180

c)

4x + 1 + 4x + 1 + 5x - 4 = 180

d)

4x + 1 + 5x - 4 + 5x - 4 = 180

105.

What is the length of DF?

a)

8

b)

4

c)

25

d)

71

106.

Is DE 1/2 the length of BC?

a)

Yes

b)

No

107.

Which of the following describes a median of a triangle?

a)

A. A middle of the triangle.

b)

B. A segment with endpoints at the vertex and midpoint of the opposite side.

c)

C. A segment that connects two midpoints of two sides.

d)

D. A segment that connects the vertex and the opposite side at 90 degrees.

108.

Which of the following words describes the point shown in the figure?

a)

A. Centerpoint

b)

B. Orthocenter

c)

C. Centroid

d)

D. Midpoint

109.

AD = 12. Find AG

a)

6

b)

8

c)

18

d)

12

110.

CF, BE, and AD are the medians of the triangle. If BF =10, find AF.

a)

20

b)

10

c)

5

d)

Not Enough Information

111.

If G is the centroid of triangle ABC and AC= 32. Find the length of CE.

a)

16

b)

32

c)

48

d)

Not Enough Information

112.

If G is the centroid of triangle ABC and GF= 4. Find the length of GC.

a)

4

b)

8

c)

12

d)

Not Enough Information

113.

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

114.

BE = 15. Find EG.

a)

10

b)

5

c)

22.5

d)

20

115.

Identify the special segment that's pictured:

a)

Altitude

b)

Midsegment

c)

Median

d)

Angle Bisector

116.

A median of a triangle connects the ___________ of a side to the opposite vertex.

a)

midpoint

b)

right angle

c)

end point

d)

angle

117.

a)

9

b)

10

c)

8

d)

12

118.

a)

4

b)

6

c)

12

d)

8

119.

a)

17

b)

27

c)

57

d)

23

120.

If G is the centroid of triangle ABC and AG= 16. Find the length of GD.

a)

8

b)

16

c)

24

d)

Not Enough Information

121.

If G is the centroid of triangle ABC and GE= 7. Find the length of BE.

a)

7

b)

14

c)

21

d)

Not Enough Informaion

122.

[Median and Centroid]
If LB = 4, what is CL?

a)

4

b)

8

c)

6

d)

10

123.

[Median and Centroid]
If NP = 5, what is CP?

a)

5

b)

8

c)

12

d)

10

124.

The centroid cuts each median into two segments. The shorter segment is ___________ the length of the entire segment.

a)

one third

b)

two thirds

c)

three fourths

d)

one half

125.

What is point J called?

a)

centroid

b)

incenter

c)

circumcenter

d)

orthocenter

126.

GT is a Median: find FE

a)

16

b)

32

c)

11

d)

26

127.

KL is a Median: Find LJ

a)

6

b)

5

c)

3

d)

9

128.

a)

11

b)

22

c)

5.5

d)

3.67

129.

a)

10.3

b)

9

c)

3

d)

12

130.

If ZO=24 and SZ=3a-9, what is the value of a?

a)

11

b)

19

c)

21

d)

7

131.

Find WR if RH = 2. Point R is a centroid

Round your answer to the first decimal place if needed.

a)

4

b)

2

c)

8

d)

1

132.

Find QJ if WQ = 5. Point Q is a centroid

Round your answer to the first decimal place if needed.

a)

2.5

b)

5

c)

10

d)

15

133.

Find DY if DR = 16.5 Point Y is a centroid

Round your answer to the first decimal place if needed.

a)

11

b)

16.5

c)

8.25

d)

33

134.

Find QM if MC = 7. Point M is a centroid

Round your answer to the first decimal place if needed.

a)

14

b)

7

c)

21

d)

3.5

135.

Find x if JV = 3x - 6 and VE = 2x - 7. Point V is a centroid

Round your answer to the first decimal place if needed.

a)

x = 8

b)

x = 10

c)

x = 3

d)

x = 5

136.

Solve for x. Point L is a centroid

Round your answer to the first decimal place if needed.

a)

x = 5

b)

x = 2

c)

x = 10

d)

x = 7

Triangle Angle and Length Theorems Review

Total questions: 136

Worksheet time: 3hrs 31mins

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