Geometry Final Exam

Geometry Final Exam Review

By Dr. Tom Giles

Multiple Choice

RM=

• RM=6
• RM=3
• RM=12
• RM=9

Multiple Choice

Write the equation of the line parallel to y = 4x + 3 and passing through the point (-4, -5)

• y = - 1/4x - 6

• y = - 1/4x + 8

• y = 4x -2

• y = 4x + 11

Multiple Choice

Find AC

• 7
• 8
• 22
• 23

Multiple Choice

What is the measure of the exterior angle?

• 9

• 52

• 28

• 15

Multiple Choice

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

• (5, -2)
• (10, -6)
• (5, -3)
• (2, -2)

Multiple Choice

Find the midpoint between G( -1, 2) and H( -3, - 4)

• $$\left(\frac{1}{2},-\frac{7}{2}\right)$$

• $$\left(-2,-1\right)$$

• $$\left(-4,-2\right)$$

• $$\left(1,3\right)$$

Multiple Choice

Find the midpoint of the segment with the endpoints:  (-2, 6) and (-3, 7)   

• (0.5, 0.5)
• (6.5, -2.5)
• (-1.5, 7)
• (-2.5, 6.5)

Multiple Choice

Which of the following can be used to prove the triangles congruent?

• SSS

• ASA

• SAS

• SSA

Multiple Choice

Find the distance.

• 9.7
• 10.7
• 11.7
• 12.7

Multiple Choice

Find the value of x.

• 10

• 29

• 23

• 35

Multiple Choice

A(3,1) B(-2,-1) written correctly is:

• $$\sqrt{\left(-2-3\right)^2\ +\ \left(-1-1\right)^2}$$

• $$\sqrt{\left(1-3\right)^2\ +\ \left(-1-2\right)^2}$$

• $$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

• $$\sqrt{\left(-2-3\right)^2\ -\ \left(-1-1\right)^2}$$

Multiple Choice

Congruent by

• SSS
• SAS
• ASA
• AAS

Multiple Choice

What is the distance between (2,9) and (1,5)?

• 15
• 17
• 4.12
• 3.87

Multiple Choice

Congruent by

• SSS
• SAS
• ASA
• AAS

Multiple Choice

What type of angles are these?

• Adjacent Angles

• Linear Pair

• Complementary Angles

• Supplementary Angles

• Vertical Angles

Multiple Choice

What is the slope of the line that passes through the following points:
(9, 3) and (7, 8).

• 6
• 3
• -5/2
• 6

Multiple Choice

Which angles are vertical angles?

• $$\angle8\ \&\ \angle7$$

• $$\angle8\ \&\ \angle6$$

• $$\angle8\ \&\ \angle5$$

Multiple Choice

Find the exterior angle

• 100
• 55
• 45
• 80

Multiple Choice

Solve for x.

• 16
• 11
• 50
• 6

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 1
• 11
• 7
• 6

Multiple Choice

What type of angle is shown?

• acute
• obtuse
• right
• straight

Multiple Choice

Write an equation of a line that passes through the point (-2, 4) and is perpendicular to the line y = 2x − 8.

• $$y=2x+8$$

• $$y=-\frac{1}{2}x-3$$

• $$y=2x$$

• $$y=-\frac{1}{2}x+3$$

Multiple Choice

Find the value of ∠A.

• 25°
• 30°
• 35°
• 90°

Multiple Choice

Determine if the following numbers can represent the side lengths of a triangle. If so, determine if the triangle is acute, obtuse or right.

4, 7, 10

• Acute Triangle

• Obtuse Triangle

• Right Triangle

• No Triangle can be Formed

Multiple Choice

Find $$m\angle2.$$  

• $$65\degree$$  

• $$180\degree$$  

• $$115\degree$$  

Multiple Choice

A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feet on the wall. Find to the nearest degree, the angle the ladder makes with the wall.

• $$22\degree$$

• $$66\degree$$

• $$24\degree$$

• $$37\degree$$

Multiple Choice

A single angle that measures between 90 and 180 degrees.

• Obtuse Angle
• Acute Angle
• Right Angle
• Linear Pair

Multiple Choice

The triangles are similar. Find the value of x.

• A
• B
• C
• D

Multiple Choice

Calculate m∠ABC.

• 45°

• 60°

• 105°

• 15°

Multiple Choice

Write the equation of the line parallel to y = 4x + 3 and passing through the point (-4, -5)

• y = -1/4x - 6

• y = -1/4x + 8

• y = 4x - 2

• y = 4x + 11

Multiple Choice

Angle 3 and Angle 6 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

Multiple Choice

Solve for x

• 19

• 6

• 38

• 32

Multiple Choice

Which of the following angles would NOT be congruent to the measure of $$\angle7$$ ?

• $$\angle2$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle8$$  

Multiple Choice

What is the distance between (3,1) and (6, 8)

• 12.73
• 18
• 3.16
• 7.07

Multiple Choice

If the  $$m\angle7\ =\ 115\degree,$$  find the measure of  $$\angle2.$$  

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Which of the following is NOT an acceptable way to prove triangles congruent?

• SSS

• ASA

• AAA

• SAS

Multiple Choice

The angle relationship shown is - 

• complementary angles
• supplementary angles
• vertical angles
• adjacent angles

Multiple Choice

What is the value of angle F?

• 9
• 12
• 90
• 110

Multiple Choice

If m∠1 = 30°, then m∠3 = 

• 30°
• 60°
• 150°
• undetermined

Multiple Choice

What is the length of BC?

• 6

• 31

• 29

• 11

Multiple Choice

Which of the following terms best describes Angle d?

• Remote interior angle
• Corresponding angle
• Exterior angle
• Interior angle

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 1
• 5
• 2

Multiple Choice

What is the measure of angle b?

• 36^o
• 56^o
• 63^o
• 117^o

Multiple Choice

Find the value of x:

• 58.3
• 1.7
• 21
• 18

Multiple Choice

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

• 180
• 90
• 360
• 270

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

Find the measure of angle x.

• 138
• 96
• 93
• 87

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Multiple Select

• A
• B
• C
• D

Multiple Choice

How do these triangles appear to be similar?

• AA
• SAS
• SSS
• Not Similar

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Solve for X.

• 100° 
• 110° 
• 150° 
• 168° 

Multiple Choice

• A
• B
• C
• D

Multiple Choice

 What is the name of this polygon?

• a pentagon
• a quadrilateral
• an octagon
• a triangle

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Find the angle sum of the polygon.

• 720° 
• 900° 
• 1080° 
• 1260° 

Multiple Choice

Are these triangles congruent?

• Yes, by AAS
• Yes, by SAS
• Yes, by ASA
• No, this is the SSA one!!

Multiple Choice

The cube has a side length of 7 inches.  What is its volume?

• 343 
• 21
• 49
• 294

Multiple Choice

Use the congruency statement to answer the following: 
<F = ___

• <H
• <I
• <G
• not congruent to another angle

Multiple Choice

What is the measure of one exterior angle of a regular octagon?

• $$135\degree$$

• $$1080\degree$$

• $$60\degree$$

• $$45\degree$$

Multiple Choice

The two triangles are congruent. Find the value of c.

(Diagrams are not to scale.)

• 4

• 5

• 3

• 38

Multiple Choice

Find missing side

• 5
• 7
• 9
• 11

Multiple Choice

If ∆MNO ≅ ∆PQR, which of the following can you NOT conclude as being true? [Hint: DRAW A PICTURE!!]

• MN = PR

• ∠M ≅ ∠P

• NO = QR

• ∠N ≅ ∠Q

Multiple Choice

Use the figure to solve for x

• 13

• 12

• 15

• 14

Multiple Choice

What is Dilation?

• Dilation means to enlarge or reduce a shape

• Dilation means to flip over a line

• Dilation means two figures that look alike

• Dilation means to make a shape smaller

Multiple Choice

What does congruent mean?

• Same shape, different size
• Not same shape, or size
• Same size, same shape

Multiple Choice

Are these two figures congruent, similar or neither?

• Congruent

• Neither

• Similar

Multiple Choice

Solve for x.

• 5

• 16.97

• 17.69

• 25

Multiple Choice

Choose the correct scale factor:

• 2.5

• 1.5

• 3.5

• 4

Multiple Choice

• A

• B

• C

• D

Multiple Choice

If two figures are similar, the corresponding angles are...

• Congruent

• Supplementary

• Proportional

• Different

Multiple Choice

Find the value of x in the diagram.

• 10

• 4

• 6

• 7

Multiple Choice

Which scale factor would enlarge a figure?

• 3.5

• 0.5

• 1/3

• 5/8

Multiple Choice

True or false: The pythagorean theorem works for all triangles.

• True

• False, only works for right angles

• False, only works for acute angles

• False, only works for quadrilaterals

Multiple Choice

How does a dilation change the angles of a polygon?

• It changes by the scale factor.
• Dilations do not change the angles.
• It is impossible to answer this question.  The angles change unpredictably.
• The angles all change to larger angles.

Multiple Choice

The exterior angles of a polygon add up to __________________.

• 180

• (n - 2)*180

• 360

• (n - 2)*360

Multiple Choice

If two figures are similar, the corresponding sides are ______________.

• equal
• congruent
• proportional
• none of these

Multiple Choice

The interior angles of a polygon add up to equal ___________________.

• 360

• (n - 2)*180

• (n - 2)*360

• 180

Multiple Choice

Tell whether the two figures are congruent or similar.

• Congruent, because their sides are the same.

• Congruent, because their sides are proportional.

• Similar, because their sides are the same.

• Similar, because their sides are proportional.

• They are neither congruent or similar.

Multiple Choice

Which number is a square root of 400?

• 400

• 200

• 40

• 20

Multiple Choice

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

• Yes
• No
• I don't know.

Multiple Choice

A right triangle has a hypotenuse of 15m and one of the sides is 9m. What is the length of the missing side?

• 6m

• 8m

• 4m

• 12m

Multiple Choice

Can the sides of a triangle have lengths 3, 4, and 9?

• Yes
• No

Multiple Choice

A triangle has sides of 48mm, 55mm and 73mm. Is it a right triangle?

• Yes, because 48²+55² = 73².

• Yes, because 48+55>73.

• No, because 48+55 does not equal 73

• No, because we do not know which is the hypotenuse.

Multiple Choice

Which of these sets of angles will make a triangle?

• 44 $$\degree$$ , 55 $$\degree$$ , 66 $$\degree$$

• 19undefined, 28undefined , 37undefined

• 91undefined, 82undefined , 73undefined

• 70undefined, 65undefined , 45undefined

Multiple Choice

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

N ( -4, -3 )

J ( -2, -5 )

• 2

• 2.8

• 10

• 5.3

Multiple Choice

Complete the Theorem:

"The sum of the measures of the two smallest sides of a triangle...

• ...will equal the measure of the third side.

• ...cannot be more than the measure of the third side.

• ...must be greater than the measure of the third side.

• ...has nothing to do with the third side.

Multiple Choice

If the sum of the interior angles of a polygon equals 900°, how many sides does the polygon have? 

• 7
• 9
• 10
• 12

Multiple Choice

Find the interior angle sum for each polygon. Round your answer to the nearest tenth if

necessary.

• A

• B

• C

• D

Multiple Choice

What is the sum of the exterior angles of a decagon

• 1440
• 360
• 540
• 720

Multiple Choice

Find the measure of one interior angle in each regular polygon. Round your answer to the

nearest tenth if necessary.

• A

• B

• C

• D

Multiple Choice

Find the sum of interior angles in a heptagon

• 900
• 720
• 540
• 180

Multiple Select

What is a regular polygon? (you may choose more than one answer)

• all side lengths are the same length

• all angles are the same (equal in measure)

• only some side lengths are the same

• all side lengths are different

• only some angles are the same

Multiple Choice

What is the SUM of the exterior angles of a 20-gon?

• 180

• 360

• 3240

• 162

Multiple Choice

Find the missing angle.

• 75
• 85
• 100
• 45

Multiple Choice

What is the measure of each interior angle of a regular octagon?

• 135

• 180

• 145

• 190

Multiple Choice

Find the value of X

• 94
• 25
• 36
• 180

Multiple Choice

The measures of one interior angle of a regular polygon is 140^o. What is the name of the polygon?

• Decagon

• Nonagon

• Heptagon

• Hexagon

Multiple Choice

The opposite angles of a parallelogram are ...

• complementary
• congruent
• supplementary
• perpendicular

Multiple Choice

Do the segment lengths 15, 12, and 9 form a right triangle?

• Yes
• No
• Maybe
• Pythagoras

Multiple Choice

In a parallelogram, consecutive angles are __________.

• congruent
• supplementary
• corresponding
• parallel

Multiple Choice

Solve the proportion.
____ = ____

• p=31.3
• p=308
• p=924
• p=532

Multiple Choice

In a parallelogram, diagonals are __________.

• perpendicular
• bisected
• congruent
• parallel

Multiple Select

How can a square be classified? Select ALL that apply.

• Rectangle

• Parallelogram

• Rhombus

• Trapezoid

Multiple Choice

Find m∠U.

• 95°
• 85°
• 75°
• 90°

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

Find x.

• 103
• 77
• 83
• 73

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Select

CHECK ALL THAT APPLY:

All sides are congruent.

• Parallelograms

• Rhombuses

• Rectangles

• Squares

Multiple Choice

Does a triangle with these side lengths exist?
18, 22, 5

• Yes
• No
• I don't know.

Multiple Choice

TRUE OR FALSE:

Squares, rhombuses, and rectangles are considered parallelograms.

• True

• False

Multiple Choice

Which is NOT a property of a parallelogram?

• Diagonals bisect each other
• Diagonals are congruent
• Both pairs of opposite sides are parallel
• Both pairs of opposite angles are congruent

Multiple Choice

TRUE OR FALSE:

A parallelogram is always a rectangle.

• True

• False

Multiple Choice

Which shape is NOT a type of parallelogram?

• trapezoid
• rectangle
• rhombus
• square

Multiple Choice

A Trapezoid is a parallelogram.

• True

• False

Multiple Choice

The figure is a parallelogram.  
Solve for x.  

• 7
• 2
• 0
• 4

Multiple Choice

In a Trapezoid, there is exactly ___ pair(s) of parallel sides.

• 1

• 2

• 3

• 4

Multiple Choice

A rhombus is a parallelogram.

• Always
• Sometimes
• Never

Multiple Choice

The legs of an isosceles trapezoid are _____.

• parallel
• perpendicular
• congruent
• skew

Multiple Choice

If ABCD is a parallelogram, what is the length of BD? 

• 10
• 11
• 7
• 5

Multiple Choice

In a Trapezoid, the parallel sides are called the _____________.

• Legs

• Bases

Multiple Choice

LMNO is a parallelogram
solve for X

• 19
• 20
• 33
• 53

Multiple Choice

Find the measure of ∠1:

• 79°
• 101°
• 72°
• 180°

Multiple Choice

If PN = 2x + 5, ON = x + 3, and OS = 3x - 2. Solve for PS.

• 7 units

• 10 units

• 17 units

• 19 units

Multiple Choice

Base angles of an isosceles trapezoid are _____.

• neither
• supplementary
• congruent

Multiple Choice

In order to show a figure is a square, you need to show it is a ...

• Rhombus

• Rectangle

• Parallelogram

• Parallelogram, Rhombus AND Rectangle

Multiple Choice

Find the measure of the midsegment XY:

• 21
• 9
• 12
• 10.5

Multiple Choice

$$\sqrt{120}$$  

• $$2\sqrt{30}$$  

• $$4\sqrt{30}$$  

• $$\sqrt{12}\sqrt{10}$$  

• $$24\sqrt{5}$$  

Multiple Select

Which of the following statements are true?

• BD and AC are perpendicular

• BD and AC are congruent

• ∠A and ∠C are congruent

• AD and DC are congruent

Multiple Choice

Simplify $$\sqrt{125}$$  

• $$3\sqrt{5}$$  

• $$5\sqrt{5}$$  

• $$3\sqrt{25}$$  

• $$5\sqrt{3}$$  

Multiple Choice

Level 1

The Pythagorean Theorem ONLY works on which triangle?

• obtuse

• scalene

• isosceles

• right

Multiple Choice

Simplify $$\sqrt{32}$$  

• $$2\sqrt{8}$$  

• $$4\sqrt{2}$$  

• $$16\sqrt{2}$$  

• $$2\sqrt{4}$$  

Multiple Choice

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

• $$17^2+8^2=b^2$$

• $$8^2+b^2=17^2$$

• $$17^2+b^2=8^2$$

• $$\frac{8^2}{b^2}=\frac{17^2}{100}$$

Multiple Choice

$$\sqrt{75}$$  

• $$5\sqrt{3}$$  

• $$3\sqrt{5}$$  

• $$25\sqrt{3}$$  

• $$5\sqrt{15}$$  

Multiple Choice

The longest side of a right triangle is DIRECTLY ACROSS from the...

• right angle.
• acute angle.
• obtuse angle.

Multiple Choice

$$\sqrt{80}$$  

• $$4\sqrt{5}$$  

• $$5\sqrt{4}$$  

• $$16\sqrt{5}$$  

• $$2\sqrt{20}$$  

Multiple Choice

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

• Divide both sides by 2
• Take the square root of both sides

Multiple Choice

If ∆XYZ ≅ ∆KLM, then
∠Y≅ _____

• ∠K
• ∠M
• ∠L
• ∠Z

Multiple Choice

solve for c

• 7
• 9
• 4
• 13

Multiple Choice

Complete the congruence statement.

• CRP
• PCR
• RPC
• PRC

Multiple Choice

Find the perimeter of the shape.

• 27 ft.

• 40 ft.

• 27 ft.

• 54 ft.

Multiple Choice

What is the longest side of a right triangle called?

• Leg A
• Leg B
• Hypotenuse
• Pythagoras' Big Buddy

Multiple Choice

What is the diameter?

• 5 in
• 10 in
• 3.14 in
• 15.84 in

Multiple Choice

a = 2.1, b = 7.2,
c = 7.5
Is this a right triangle?

• yes 
• no

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter
• Radius

Multiple Choice

The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
11, 12, 15

• right
• obtuse
• acute

Multiple Choice

What is the circumference of a 12-inch pizza?

• 37.68 inches
• 18.84 inches
• 113.04 inches
• 432.16 inches

Multiple Choice

Find the measure of $$\overline{QA}$$  

• 4

• -4

• 16

• 28

Multiple Choice

An angle in a circle with vertex on the center of the circle

• Central angle
• Angle
• Inscribed angle
• Circle

Multiple Choice

Find the missing length if the proportion is $$\frac{12}{x}=\frac{20}{25}$$  

• 25

• 15

• 6

• 16

Multiple Select

The inscribed angle is  (choose 3 correct answers)

• $$\angle DCB$$  

• $$\angle BAD$$  

• $$\angle CDA$$  

• $$\angle CBA$$  

Multiple Choice

What is the measure of the indicated arc?

• 70

• 140

• 35

• 90

Multiple Choice

Find the measure of arc AB.

• 17
• 34
• 68
• 146

Multiple Choice

Find m∠PRQ.

• 39°
• 90°
• 51°
• 15°

Multiple Choice

Find the measure of angle V:

• 85

• 80

• 87

• 117

Multiple Choice

What type of arc is arc AEB?

• Major

• Minor

• Semi-circle

• Noah's

Multiple Choice

How many degrees are in a circle?

• 90
• 180
• 270
• 360

Multiple Choice

Which shows a tangent line?