Free Printable Geometry midterm review

1.

Which illustration shows the correct construction of an angle bisector?

a)

b)

c)

d)

2.

Which geometric principle is used to justify the construction?

a)

A line perpendicular to one of two parallel lines is perpendicular to the other.

b)

Two lines are perpendicular if they intersect to form congruent adjacent angles.

c)

When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel.

d)

When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.

3.

In △ABC, m∠A = 3x + 1, m∠B = 4x - 17, and m∠C = 5x - 20. Which type of triangle is △ABC?

a)

Right

b)

Scalene

c)

Isosceles

d)

Equilateral

4.

Natalie is playing with the pinwheel like the one shown in the picture above. Which degree of rotation would carry the pinwheel onto itself?

a)

5°

b)

125°

c)

216°

d)

225°

5.

What is the measure of angle b?

a)

36^o

b)

56^o

c)

63^o

d)

117^o

6.

As shown in the diagram below, CD is a median of △ABC.

Which statement is always true?

a)

AD ≅ DB

b)

AC ≅ AD

c)

∠ACD ≅ ∠CDB

d)

∠BCD ≅ ∠ACD

7.

Which transformation does not produce an image that is congruent to the original?

a)

A dilation of scale factor 1 centered at (2,4)

b)

A dilation of scale factor ½ centered at the origin

c)

A reflection over y = 4x

d)

A rotation of 270 degrees followed by a translation down 2

8.

Tina wants to sew a piece of fabric into a scarf in the shape of an isosceles triangle, as shown in the accompanying diagram.

What are the values of x and y?

a)

x = 42 and y = 96

b)

x = 69 and y = 69

c)

x = 90 and y = 48

d)

x = 96 and y = 42

9.

Given: △ABD, BC is the perpendicular bisector of AD

Which statement cannot always be proven?

a)

AC ≅ DC

b)

BC ≅ CD

c)

∠ACB ≅ ∠DCB

d)

△ABC ≅ △DBC

10.

Describe the transformation in the picture from the black triangle to the blue triangle.

a)

Reflection over the y-axis

b)

Reflection over the x-axis

c)

Reflection over y=x

d)

Reflection over y=-x

11.

What are the coordinates of the vertices of the triangle after the translation 2 units up?

a)

(1,2), (3, 5), (-3,0)

b)

(-1,2), (-3,5), (-3,0)

c)

(1,2),(-3,5),(-3,0)

12.

The triangles below are similar. Find the missing side length.

a)

x = 30

b)

x = 333

c)

x = 10.8

13.

The triangles below are similar. Find x.

a)

x = 42

b)

x = 14

c)

x = 12

d)

x = 144

14.

Find the missing length.

a)

36

b)

64

c)

10

d)

100

15.

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

a)

SAS

b)

ASA

c)

AAS

d)

Not Congruent

16.

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

a)

SSS

b)

AAS

c)

AA

d)

Not Congruent

17.

If ∆ABC ≅∆DEF, what side is congruent to CA?

a)

FE

b)

DE

c)

FD

d)

DF

18.

Describe the angle relationship.

a)

Same Side Interior

b)

Corresponding

c)

Alternate Interior

d)

Alternate Exterior

19.

Which of the following statements correctly describes perpendicular lines?

a)

Coplanar but do not intersect

b)

Coplanar and intersect at 90 degree angle

c)

Coplanar and intersect at either obtuse or acute angles

d)

Not coplanar

20.

If ∠DEF and ∠HIJ are a linear pair, which of the following is not always true?

a)

They are adjacent.

b)

They are complementary.

c)

They are supplementary.

d)

They are on a line together.

21.

Converse of the statement: If p, then q.

a)

If p, then q.

b)

If q, then p.

c)

If ~ (not) p, then ~ (not) q.

d)

If ~ (not) q, then ~ (not) p.

22.

Inverse of the statement: If p, then q.

a)

If p, then q.

b)

If q, then p.

c)

If ~ (not) p, then ~ (not) q.

d)

If ~ (not) q, then ~ (not) p.

23.

Contrapositive of the statement: If p, then q.

a)

If p, then q.

b)

If q, then p.

c)

If ~ (not) p, then ~ (not) q.

d)

If ~ (not) q, then ~ (not) p.

24.

Two lines that do not intersect and are not parallel

a)

Perpendicular lines

b)

Transversals

c)

Skew lines

d)

Parallel lines

25.

Lines that passes through two lines in the same plane at two distinct points

a)

Perpendicular lines

b)

Transversals

c)

Skew lines

d)

Parallel lines

26.

How can you determine the distance between two points?

a)

Use the midpoint formula

b)

Graph the points and use the Pythagorean Theorem

c)

Both 1 & 2

d)

None of the above

27.

What is the midpoint formula?

a)

$\left(\frac{x^1+x^2}{2},\frac{y^1+y^2}{2}\right)$

b)

$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$

c)

$y-y_1=m\left(x-x_2\right)$

d)

$m=\frac{y_2-y_1}{x_2-x_1}$

28.

What is the distance formula?

a)

$\left(\frac{x^1+x^2}{2},\frac{y^1+y^2}{2}\right)$

b)

$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$

c)

$y-y_1=m\left(x-x_2\right)$

d)

$m=\frac{y_2-y_1}{x_2-x_1}$

29.

Term for a polygon whose vertex angles are congruent

a)

equilateral

b)

convex

c)

regular

d)

equiangular

30.

Term for a polygon whose sides measurements are congruent

a)

equilateral

b)

convex

c)

regular

d)

equiangular

31.

A line segment joining a vertex to the midpoint of the opposite side

a)

altitude

b)

median

c)

angle bisector

d)

perpendicular bisector

32.

a)

A

b)

B

c)

C

d)

D

33.

What is the midpoint between (3, -1) and (7, -5)?

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

34.

What is the value of x?

a)

60

b)

26

c)

14

d)

10

35.

How do you know lines are parallel?

a)

Slopes are opposite reciprocals of each other

b)

Slopes are the same

36.

The slope of perpendicular lines are:

a)

equal

b)

negative

c)

negative reciprocals

37.

a)

Choice (1)

b)

Choice (2)

c)

Choice (3)

d)

Choice (4)

38.

a)

Choice (1)

b)

Choice (2)

c)

Choice (3)

d)

Choice (4)

39.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

40.

Take a guess! Which one is the correct construction for a perpendicular bisector?

a)

1

b)

2

c)

3

d)

4

41.

Name that shape.

a)

quadrilateral, rectangle

b)

quadrilateral, rectangle, square

c)

quadrilateral, parallelogram, rectangle

d)

quadrilateral, parallelogram, rectangle, square

42.

Find the length of DE

a)

12

b)

11

c)

10

d)

13

43.

If m∠XOZ = 74°, find m∠XOY.

a)

37°

b)

74°

c)

90°

d)

148°

44.

Solve for x

a)

6

b)

140

c)

20

d)

90

45.

Tell whether the angles are complementary or supplementary. Then find the value of x.

a)

Complementary; x=25

b)

Complementary; x=5

c)

Supplementary; x=25

d)

Supplementary; x=5

46.

What is m∠ABD

a)

80

b)

120

c)

20

d)

100

47.

Q is the midpoint of PR.
PQ = 6x – 7 and QR = 5x + 1.
Find the length of PR.

a)

8

b)

16

c)

41

d)

82

48.

A flip is also called a __________

a)

Translation

b)

Rotation

c)

Reflection

d)

Transformation

49.

If a figure is in the 2nd quadrant and you are rotating 180 deg., which quadrant would you be in.

a)

1st quadrant

b)

2nd quadrant

c)

3rd quadrant

d)

4th quadrant

50.

Name the image of C(6, -4) under a rotation 90 degrees about the origin.

a)

C'(4, 6)

b)

C'(-4, -6)

c)

C'(6, 4)

d)

C'(-6, -4)

51.

Write a rule for the translation.

a)

(x -1, y + 2)

b)

(x -2, y + 1)

c)

(x +2, y - 1)

d)

(x +1, y - 2)

52.

Find the distance between (-4, 5) and (7, 18) after a translation three units right and two units up.

a)

15.96

b)

16.08

c)

16.23

d)

17.03

53.

Which transformation is not a rigid motion?

a)

Translation 2 units left.

b)

Rotation 90 degrees counter clockwise.

c)

Reflection over the y-axis.

d)

Dilation with a scale factor of 1/2.

54.

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?

a)

24 Weeks

b)

24-ounce bottle

c)

10.6 Weeks

d)

10.6-ounce bottle

55.

A model of a car is 3 in wide and 2 in tall. The actual car is 4 ft wide, how tall would it be?

a)

3.5

b)

4

c)

5

d)

2.6

56.

Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, what is the actual distance between the 2 cities?

a)

87 km

b)

216 km

c)

33 km

d)

192 km

57.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

58.

What is the slope in the equation y=2x + 3?

a)

2

b)

3

c)

5

d)

Cannot be Determined

59.

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

a)

Parallel

b)

Perpendicular

c)

Neither

60.

Write equation of a line in point slope form that passes through (3,8) and has a slope of 5?

a)

y-8=5(x-3)

b)

y=5x+8

c)

y-3=5(x-8)

d)

y-y₁₌ m(x-x₁₎

61.

Write an equation in point slope form of equation of line

point (7,10) and has a slope of -2?

a)

y-10 = -2(x+7)

b)

y-10 = -2(x-7)

c)

y+10 = -2(x+10)

d)

y -10 = -2x+2

62.

Is DE parallel to BC?

a)

Yes

b)

No

63.

Find the length of AB

a)

6

b)

11

c)

17

d)

68

64.

What is the value of x?

a)

10

b)

No Solution

c)

5

d)

2

65.

What is the measure of angle a?

a)

50

b)

80

c)

130

d)

Cannot Determine

66.

What is the justification (reason)?

a)

Reflexive Property

b)

Symmetric Property

c)

Transitive Property

d)

Substitution

67.

What is the justification (reason)?

a)

reflexive property

b)

definition of segment bisect

c)

definition of a midpoint

d)

substitution property

68.

Which of the following is NOT a triangle congruence criteria?

a)

SAS

b)

AAS

c)

SSA

d)

ASA

69.

What does CPCTC stand for?

a)

Corresponding Parts of Congruent Triangles are Congruent

b)

Congruent Parts of Congruent Triangles are Corresponding

c)

Colorful Pieces of Corresponding Triangles are Congruent

d)

Congruent Pieces of Congruent Triangles are Congruent

70.

What triangle congruence criteria is shown in the given diagram?

a)

AAS

b)

ASA

c)

SSA

d)

SAS

71.

What is the missing piece of information required to prove these triangles congruent?

a)

QY ≅ QY

b)

NY ≅ PY

c)

∠N ≅ ∠P

d)

QY is the perpendicular bisector

72.

Identify the property of equality.
If 9=x, then x=9

a)

Reflexive

b)

Symmetric

c)

Transitive

d)

Substitution

73.

What is Addition property of equality

a)

a. If a=b, then a+c=b+c

b)

b. If a=b, then a-c=b-c

c)

c. If a=b, then ac=bc

d)

d. If a=b, then a/c=b/c

74.

Step 2 is what

a)

Substitution property (simplify)

b)

Multiplication property of equality

c)

Division property of equality

d)

Distributive Property

75.

What is step 4

a)

Substitution property (simplify)

b)

Addition property of equality

c)

Subtraction property of equality

76.

Step 1 is what

a)

addition property of equality

b)

given

c)

subtraction property of equality

d)

prove

77.

What is the formula used to solve for the hypotenuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

78.

_{^{Find the missing side}}

a)

36

b)

76.8

c)

12

d)

40

79.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

80.

Can the following side measures form a triangle?
3, 5, 8

a)

Yes

b)

No

81.

Does a triangle with these side lengths exist?
15, 12, 9

a)

Yes

b)

No

c)

I don't know.

82.

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

a)

more than 6 but less than 20

b)

more than 20 but less than 6

c)

less than 6 but more than 20

83.

Identify the longest side measure.

a)

LM

b)

MQ

c)

LQ

84.

A continuous straight extent of length, without breadth or thickness is called a ________________. It also has arrowheads on both sides.

a)

line

b)

ray

c)

line segment

d)

linear pair

85.

Points that lie in the same plane are called ____________________.

a)

coplanar points

b)

collinear points

c)

line segment

d)

defined terms

86.

A _______________ is a flat, 2-dimensional surface usually represented by a shape that looks like a floor or a wall.

a)

plane

b)

segment bisector

c)

line

d)

ray

87.

A __________________ is an object that has no dimension. It is usually represented with a dot that identifies an exact location in space.

a)

point

b)

line

c)

line segment

88.

What is the sum of the interior angles of the nonagon shown?

a)

720°

b)

900°

c)

1080°

d)

1260°

89.

What is the sum of the interior angles for a 24-gon?

a)

3960

b)

360

c)

15

d)

4280

90.

Calculate the sum of the interior angle measures of a polygon with 16 sides.

a)

2880 degrees

b)

2520 degrees

c)

344 degrees

d)

360 degrees

91.

What is the formula for the sum of the interior angles of a polygon?

a)

S=360

b)

S=(n-2)180

c)

n=360/ext. angle

d)

1 int. angle + 1 ext. angle=180

92.

geometry means

a)

earth measure

b)

brain injury

c)

measure across

d)

side measure

Geometry midterm review

Total questions: 92

Worksheet time: 3hrs 36mins

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