Vocabulary/Concepts to Know

Page 1

REVIEW

Chapter 6

Vocabulary/concepts to know:

polygonside of a polygonvertex of a polygon

convexnonconvex, concaveequilateral polygon

equiangular polygonregular polygondiagonal of a polygon

parallelogramrhombusrectangle

squaretrapezoidbase of a trapezoid

legs of a trapezoidbase angles of a trapezoidisosceles trapezoid

midsegment of a trapezoidkite

1.Which of the following does not represent a polygon?

I.II.III.

IV.V.

A.I, II, and IV onlyB.I and II only

C.I, III, and V onlyD.III and V only

E.II and IV only

2.Which term(s) below best describe the polygon?

I.EquilateralII.Equiangular

III.ConvexIV.Concave

A.I and III

B.III only

C.I and IV

D.I, II, and III

3.Which term(s) below best describe the polygon?

I.EquilateralII.Equiangular

III.ConvexIV.Concave

A.I and III

B.I and IV

C.I, II, and IV

D.IV only

4.Which of the following shows a concave hexagon?

I. II. III. IV. V. VI.

A.I and II onlyB.III and VI only

C.V onlyD.IV only

E.III, V, and VI only

5.Find the value of y.

A.60

B.65

C.111

D.116

6.What is the most precise name for the figure?

A.parallelogram

B.rectangle

C.rhombus

D.square

7.The diagonals are always perpendicular to each other in a _____.

A.rectangle

B.rhombus

C.parallelogram

D.trapezoid

8.In Rhombus WXYZ find m<Y.

A.10

B.22

D.96

E.122

9.FORD is a quadrilateral. Which information would not allow you to conclude that FORD is a parallelogram?

A.FO || RD and OR || FD

B.F R and O D

C.FO  OR and RD  FD

D.mF = 25, mO = 155, mR = 25

E.FO || DR and FO  DR

10.Quad. MESA is a rectangle. If MS and EA bisect each other at N and MN  AN. MESA must be a

I.parallelogramII.rectangleIII.square

A.I onlyB.II only

C.I and IID.II and III

E.I, II, and III

11.Quadrilateral FIVE is a square. If FA = x + 4 and IE = 4x – 10, find FV.

B.9

C.13

D.26

12.In quadrilateral MATH, M is supplementary to A but A is not supplementary to T. Quad. MATH is a _____?

I.trapezoidII.parallelogramIIIsquare

A.I onlyB.II only

C.II or IIID.I or II

E.I, II, or III

13.If MATH is a parallelogram, then which of the following must be true?

A.M  H

B.MA  HM

C.MA  AT

D.mA + mT = 180

14.Suppose you want to prove the theorem below using the figure below. What is the Given statement in the proof?

"If the diagonals of a quadrilateral bisect each other,

then the quadrilateral is a parallelogram."

A.ASEM is a parallelogram

B.AE = MS

C.AB = BE and BS = MB

D.AB = BS and BE = MB

15.Which of the following figures are parallelograms?

I.II.III.IV.

A.III only

B.II and IV only

C.I, II, and IV only

D.I, II, III, and IV only

16.Using the figure at the right, which of the following statements can be

used to prove that quad. CHEV is a parallelogram?

A.HV = CE

B.CH = EV and CHE HEV

C.CVH EHV

D.CH = EV and HCE CEV

17.CHEV is a parallelogram. If HY = 2(2x + 3), CY = 10,

and VY = 18, what is the value of x?

A.3

B.3.75

C.5.25

D.6

18.Which of the following pairs of conditions will not be sufficient to prove that quad. FORD is a parallelogram?

I.FO || RDII. FO  RD

III.OR  FDIV.F is supplementary to O.

A.I and IIB.I and III

C.II and IIID.I and IV

E.III and IV

19.What is sufficient to prove that RMHS is a parallelogram?

I.RH bisects MS.II.RM  HS; RM || HS

III.RM  HS; MH  RSIV.SRM MHS and RMH HSR

A.I and III

B.II and IV

C.II and III

D.I and IV

E.II, III, and IV

20.In the diagram KITE is a kite. Choose the statement below that is true about the given value.

A.x > y

B.x < y

C.x = y

D.The relationship cannot be determined

With the given information.

21.The area of the kite is 432 square inches. Find the length of KT.

A.6 in.

B.12 in.

C.24 in.

D.48 in.

22.Quad. ZOID is an isosceles trapezoid with

ZO || ID. Find the value of x.

A.21

B.27

C.51

23.ZOID is a trapezoid. Which of the following statements is true?

A.mO= 52

B.D O

C.D and O are supplementary

D.O and Z are supplementary

24.MATH is a rhombus. What are the values of x and y?

A.x = 6, y = 3

B.x = 6, y = 4

C.x = 3, y = 3

D.x = 3, y = 6

25.To prove that a quadrilateral is a parallelogram show that

I.both pairs of opposite angles are congruent.

II.it has one pair of congruent sides.

III.the diagonals bisect each other.

IV.the diagonals are congruent.

A.I onlyB.III only

C.I and III onlyD.I, II, III only

E.I, II, III, and IV

26.The lengths of the bases of trapezoid MATH are 14" and 20". What is the length of the midsegment of trapezoid MATH.

A.17"B.18"

C.20"D.34"

27.Which trapezoid has an 8-inch midsegment?

A.B.

C.D.

28.Choose the parallelogram which satisfies the definition of a rectangle.

I. II. III. IV.

I only
I and II
I, II, and III
I, II, and IV

29.Find the true statements.

If a quadrilateral is a square, then it is a rhombus.
If a quadrilateral is a rhombus, then it is a square.
If a quadrilateral is a rhombus and rectangle, then it is a square.
If a quadrilateral is a square, then it is a rectangle.

A.I only

B.I and II

I and III
I, III, IV

30.Choose the statement(s) that are always true.

Diagonals of a parallelogram bisect each other.
Opposite angles of a parallelogram are supplementary.
Opposite sides of a parallelogram are congruent.
Consecutive angles of a parallelogram are congruent.

A.I. only

B.I and III

I, II, III
I, II, III, IV

31.What is the area of the parallelogram?

A.225 cm2

B.255 cm2

C.330 cm2

D.450 cm2

E.510 cm2

32.Find the area of CAT.

A.3 square units

B.3 square units

C.21 square units

D.42 square units

33.Find the area of CAT

A.120 u2

B.125 u2

C.204 u2

D.238 u2

34.Find the area of parallelogram WXYZ.

A.60 u2

B.84 u2

C.144 u2

D.156 u2

35.What is the area of the polygon?

A.78 mm2

B.120 mm2

C.132 mm2

D.156 mm2

36.Find the area of the trapezoid.

A.544 square units

B.448 square units

C.272 square units

D.224 square units

37.Find the area of the quadrilateral ABCD.

6 square units
12 square units
24 square units

D.48 square units

38.Find the area of isosceles trapezoid TRAP if mA = 60, TR = 8, AP = 12 and TP = 4.

Chapter 8

Vocabulary/concepts to know:

ratio of a to bproportionextremes of a proportion

means of a proportiongeometric meansimilar polygons

scale factordilationenlargement

reduction

1.If , then

x = 3
x = 4
x = 7
x =

2.Which method can be used to show the triangles are similar?

A.SAS Similarity

B.AA Similarity

C.SSS Similarity

D.The triangles cannot be shown to be similar.

E.A, B, and C above

3.Which of the following could be used to prove that REX ROB.

A.AA Similarity

B.SAS Similarity

C.ASA Similarity

D.Answer cannot be determined.

4.Find the value of .

A.6

B.7.5

C.10

D.35

5.Find x.

A.9

B.15

C.20

D.45

E.60

6.ABE ACD. Which of the following statements is true?

A.ABE AEB

B.CDA ACD

C.AEB ADC

D.AE  AB

CD = 2(BE)

7.CRA CDT. If CR = 8 inches, RD = 7 inches, and CA = 6 inches, find CT.

8.If CY = 7 inches, YE = 13 inches, and EV = 5 inches, which equation could be used to find the length of HV?

9.Find AC.

A.10

B.15

C.20

D.25

10.A flagpole casts a 20-foot shadow. At the same time of day, a 5-foot girl casts a 4-foot shadow. How tall is the flagpole? Hint: Draw and label an appropriate diagram.

A.16 feet

B.20 feet

C.25 feet

D.100 feet

11.Find NQ.

12.What is the value of x?

A.8

B.9

C.10

D.12

13.What is the scale factor of DOG to D'O'G' if DO = 33, OG = 55, O'G' = 20, and D'G' = 28?

A.3:5

B.4:11

C.5:3

D.11:4

14.Find the value of x in the figure at the right.

A.x = -5

B.x = 8

C.x = 11

D.x = 14

15.John wanted to measure the height (h) of the room shown below. John is 6 feet tall.

7 ft
7.5 ft
8 ft
9 ft

16.Which triangle is not similar to any of the others?

17.Which triangle is not similar to any of the others?

18.What is the perimeter of trapezoid TRAP?

A.31.5 units

B.33 units

C.35.5 units

D.There is not enough information

to find the perimeter of

trapezoid TRAP

19.One standard photograph size is a 4 in. x 5 in. rectangle. Which of these other standard

rectangular sizes is similar to it?

2 in. x 3 in.
5 in. x 7 in.
8 in. x 10 in.
11in. x 14 in.

20.One way to show that two triangles are similar is to show that _____.

an angle of one is congruent to an angle of the other
a side of one is congruent to a side of the other
two sides of one are proportional to two sides of the other
two angles of one are congruent to two angles of the other

21.Two similar triangles have perimeters of 54 and 30 units. The shortest side on the smaller triangle is x and the corresponding side of the larger triangle is 3x – 6. Find x.

A.x = 2

B.x = 3

C.x = 4

D.x = 5

22.CAT DOG. Which of the following is not true?

23.Which proportion would you use to find x if MONQOP?

24.Use the diagram to choose the statement that is true given that ABCDE  LMNOP.

A.z > y

B.z < y

C.z = y

D.The relationship cannot

be determined from the

given information.

25.The design for a company’s logo is shown below.

A B X Y

What is the length of ZY? Round the answer to the

nearest tenth of a centimeter.

2.2 centimeters
2.6 centimeters
3.1 centimeters
4.2 centimeters

26.In which transformation is the image not necessarily congruent to the original figure?

A.dilation

B.reflection

C.rotation

D.translation

27.Which dashed figure represents a dilation of the

given quadrilateral?

A.I

B.II

C.III

28.What kind of transformation takes place if the

x and y coordinates of the vertices of the triangle

is multiplied by 2?

reflection
rotation
translation
dilation

29.What is the scale factor of the dilation (with center at the origin) show at the right of ABC to A'B'C'?

-2
2
–

30.A member of the Racing Boat Club created a design with two lightning bolts. The two bolts

in the design are related only by a translation. Which of these could be the design?

A.B

C.D.

31.In which transformation will the image have the same shape but not necessarily the same size as the original figure?

I.DilationII.Reflection

III.RotationIV.Translation

A.I onlyB.II and IV only

C.II, III, and IV onlyD.I, II, III, and IV

Chapter 9

Vocabulary/concepts to know:

Pythagorean TripleradicalRadicand

45-45-9030-60-90Trigonometric Ratio

Leg opposite an angleLeg adjacent to an angleTangent

SineCosineSolve a right triangle

Angle of Elevation

1.In which figure can you conclude that the triangles are similar?

I.II. III.IV.

A.I and III only

B.I and IV only

C.I, III, and IV only

D.I, II, III, and IV

2.The shadow of a monument is 50 feet long when the sun makes a 60o angle of elevation with level ground. What is the height of the monument?

A.50 ft

B50 ft

C.50 ft

D.100 ft

3.Find the equation that will find the height of the air balloon.

tan51o =
tan51o =
cos51o =
sin51o =

4.State the trigonometric ratio that corresponds to .

A.tan G

B.sin G

C.cos G

D.tan D

5.Express tan D as a ratio.

6.Using ABC give the ratio for tan C.

7.Which equation could you use to find the value of x?

8.A meteorologist from the U.S. National Weather Service, measures the angle of elevation of a weather balloon as 42. The balloon is 2000 m from her location as measured through her surveying equipment down her line of sight. Which expression would allow you to determine how high the balloon is above the ground?

I.2000 tan 42II.2000 sin 42

III.2000 sin 48IV.2000 cos 48

A.I only

B.II and IV only

C.III and IV only

D.I, II, and IV only

E.I, II, III, and IV

9.Find the mD to the nearest degree.

A.30

B.40

C.45

D.60

10. What is the value of x in the triangle below?

B.2

C.2

D.4

11.Which expression can be used to find the value of x in the triangle?

12.Find the value of x.

13.What is the length of the diagonal of a square whose side lengths are 7?

14.What is the length of an altitude of an equilateral triangle whose side length is 8?

15.An architect is designing a ramp for delivery trucks. A drawing of the ramp is shown on

the grid below.

What is the slope of the ramp?

16.A 15 foot utility pole must be anchored by a wire 8 feet from its base. How long is the wire from the top of the pole to the ground?

17 feet
20 feet
feet
25 feet

17.Which of the following can be the length of the sides of a 30-60-90 triangle?

A.I only

B.II only

C.III only

D.I and III only

E.I, II, and III

18. Choose the sets that could be the side lengths of a right triangle.

I.1, 2, 5II.3, 4, 5

III1, , IV.5, 12, 13

A.II only

B.II and III

II, III, IV
I, II, III, IV

19.A 13 foot ladder leans against a wall so that the base of the ladder is 5 feet from the wall. How high up on the wall will the ladder reach?

A.8 feet

B.12 feet

C. feet

D.15 feet

20.Find the area of the rectangle.

18 sq units
60 sq units
65 sq units
80 sq units

21.Use the diagram to find the value of the variables. Choose the statement that is true about the given values.

A.x > y

B.x < y

C.x = y

D.The relationship cannot

be determined from the

given information.

22.Use the diagram to find the value of the variables. Choose the statement that is true about the given values.

A.x > y

B.x < y

C.x = y

D.The relationship cannot

be determined from the

given information.

23.Which equations below are true about ABC?

I.9 = 12 – x

II.9 =

III. x =

IV.x2 – 92 = 122

A.I, II only

B.II, III only

C.III, IV only

D.II, III, and IV only

E.I, II, III, and IV

24.Which equations are true for the diagram?

I.r2 = (a + c)2

II.c2 = a2 – r2

III.p2 = a2 + c2

IV.m2 = p2 – a2

A.I and II only

B.II and III only

C.III and IV only

D.II, III, and IV only

E.I, II, III, IV

25.Find the area of ABC.

Chapter 10

Vocabulary/concepts to know:

CircleRadiusDiameter

 CirclesConcentric CirclesTangent Circles

ChordSecantTangent

Point of TangencyTangent SegmentCommon Tangent

Secant SegmentExternal Segment Arcs

Minor ArcMajor ArcMeasure of a Minor Arc

Measure of a Major ArcSemicircleCentral Angle

Inscribed AngleIntercepted Arc

Inscribed PolygonCircumscribed Polygon

1.Which of the following statements is false?

2.What is the measure of CAT?

A.22

B.32

C.58

90

3.Which figure represents a chord of circle P?

4.Which figure represents a tangent of the circle?

5.Find the value of x.

6.Find ET in circle P.

A.10

B.20

C.5

D.10

7.Use the diagram to find the value of x.

A.54

B.58

C.122

D.126

8.Use the diagram to find the m.

A.65

B.75

C.80

D.85

9.Use the diagram to find mCTO.

A.35

B.55

C.70

D.110

10.If mOWL = 70, find m.

A.70

B.110

C.140

D.220

11.Find the value of x if m = (5x + 15) and m = (13x + 3).

A.9

B.19

C.21

D.60

12.LM and LN are tangent to circle A.

Find the mMLN if mis 250.

A.55

B.70

C.110

D.140

13.Use the diagram to find the value of x.

A.2.2

B.7.2

C.8

D.10.4

14.Use the diagram to find the value of x.

C.4

D.16

15.Use the diagram to find the value of x.

CD is tangent to the circle.

A.2

B.4.4

D.14

16.Use the diagram to find the values of x and y.

A.x = 30, y = 15

B.x = 15, y = 30

C.x = 30, y = 30

D.x = 15, y = 15

17.Use the diagram to find the value of x.

B. 4

C.16

D.21

18.Find the value of x in circle A.

A.20.5

B.24.5

C.43

D.47

19.LM and LN are tangent to circle O. Find the value of x.

A.-15

B.-3

C.3

D.15

20.Assume all segments are tangent to the circle. Find the perimeter of ABC.

A.34

B.37

C.38

D.42

21.Find the equation of the circle with center (3, -5) and radius of 5.

A.(x + 3)2 + (y – 5)2 = 5

B.(x – 3)2 + (y + 5)2 = 5

C.(x + 3)2 + (y – 5)2 = 25

D.(x – 3)2 + (y + 5)2 = 25

Chapter 11

Vocabulary/concepts to know:

Center of a polygonRadius of a PolygonApothem of a Polygon

Central  of a Regular PolygonCircumferenceArc Length

Sector of a circleProbabilityGeometric Probability

Angle Measures in Polygons

1.An archaeologist discovered an ancient cutting tool. The tool is in the shape of a pentagon. She hopes to learn its use by measuring the sharpness of the cutting blade, but the blade is lodged in rock.

What is the measure, in degrees of angle x?

Note: The tool is not drawn to scale.

2.Find the value of x.

A32

3.Which of the following cannot be the sum of the interior angles of a regular polygon?

A.360

B.500

C.720

D.1440

4.What is the sum of the exterior angles of a regular pentagon?

A.180

B.360

C.540

D.720

5.A convex hexagon has interior angles that measure 120, 106, 92, 142, 160 and x. Find the value of x.

A.60

B.80

C.100

D.120

6.A convex octagon has exterior angles that measure 35, 41, 25, 55, 62, 17, and 38. What is the measure of the interior angle at the missing eighth vertex.

A.87

B.93

C.135

D.177

7.Find the area of a regular hexagon with side length 6 cm.

8.Find the area of the square with diagonal of 10 cm.

9.What is the length of the apothem in a regular hexagon whose sides measure 8 cm?

10.What is the area of a circle that has a diameter 24 cm long?

A.48  cm2

B.64  cm2

C.96  cm2

D.144  cm2

11.Find the area of circle R if AC = 18 inches.

A.9 inches2

B.18 inches2

C.81 inches2

D.162 inches2

12.The tires of an automobile have a diameter of 22 in. If the wheels revolve 15 times, how

far does the automobile move?

22 in.
22 in.
100 in.
330 in.

14.Find the area of the shaded region where AB = 16 m and XB = 10 m

A.(25 - 96) m2

B.(25 - 192) m2

C.(100 - 96) m2

D.(100 - 192) m2

15.Find the area of the shaded region if mCAB = 30 and BC = 4 m.

A.(16 - 8) m2

B.(16 - ) m2

C.(64 - 16) m2

D.(64 - ) m2

Chapter 12

Vocabulary/concepts to know:

PolyhedronVertexFaceEdge Prism Bases Lateral Faces Right Prism

Oblique PrismRegular PolyhedronConvexNet

Surface AreaLateral AreaCylinderRight Cylinder

PyramidHeight of PyramidSlant Height of PyramidRegular Pyramid

ConeHeight of Cone Slant Height of a ConeRight Cone

Volume of a SolidSphereHemisphereSimilar Solids

1.How many faces does a pentagonal pyramid have?

A.5

B.6

C.7

D.10

2.If a rectangular prism has 6 faces and 12 edges, how many vertices does it have?

A.6

B.8

C.12

D.14

3.Using Eulers Theorem which of the following polyhedron(s) can be drawn?

FacesVerticesEdges

I.71116

II.6811

III.121323

IV.5912

A.I and IV only

B.II and III only

C.I, III, and IV only

D.III and IV only

4.What is the surface area of the triangular prism at the right?

A.66 ft2

B.72 ft2

C.84 ft2

D.120 ft2

5.What shape will be made if the net below is folded along the dotted lines?

A.cube

B.hexagonal prism

C.rectangular pyramid

D.rectangular prism

6.Find the surface area of the right cylinder.

A.37 in2

B.40 in2

C.72 in2

D.96 in2

7.The surface area of the right cone is _____?

A.33 in2

B.60 in2

C.84 in2

D.96 in2

8.Which figure below is a rectangular pyramid?

I.II.III. IV.

A.I

B.II

C.III

D.IV

III and IV

9.Which solid corresponds to the net shown at the right?

10.What is the volume of the rectangular prism below?

A.162 in3

B.216 in3

C.288 in3

D.324 in3

11.Both rectangular solids shown below have the same volume.

What is the value of x?

12.A rectangular tank 16 in. by 8 in. by 4 in. is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 2 inches on a side, how many of these smaller tanks are needed?

13.The length of a box is 120 inches, the width is 14 inches, and the height is 8 inches.

What is the volume of the box?

142 cubic inches
960 cubic inches
1680 cubic inches
13440 cubic inches

14.The volume of a cylindrical container is given by the formula below. What is the

value of h in terms of the other three variables?

h = V -  - r2
h = ( - r2)
h =
h =

15. Which solid does this represent?

square prism
rectangular prism
square pyramid
cone

16. What is the height of the cylinder, x, if the volume is 36cubic ft?

3 ft
9 ft
18 ft
13 ft

17. Given the triangular prism and it net, find the total surface area.

A. 90 ft3 B. 120 ft3

C. 126 ft3

D. 132 ft3

18.Find the volume of the cone.

13 cubic cm
30 cubic cm
60 cubic cm
90 cubic cm

19.Find the volume of the cylinder.

13 cubic in
25 cubic in
144 cubic in
324 cubic in

20.The cylindrical oil tank shown below is half full.

113 cubic feet
151 cubic feet
226 cubic feet
452 cubic feet

21.How many faces and edges does the polyhedron shown have?

6 faces, 6 edges
6 faces, 12 edges
7 faces, 12 edges
9 faces, 16 edges

22.The solid shown is ______.

hexahedron
hexagon
octagon
octahedron

23.Marilyn plans to cover the three rectangular faces of the right triangular prism shown

below with fabric.

Note: The figure is not drawn to scale.

How many square feet of fabric will Marilyn need to cover the rectangular faces of the prism?

56 square feet
72 square feet
96 square feet

D.108 square feet

24.The volume of a sphere is 36 ft3. Find the radius of this sphere.

A.3 ft

B.6 ft

C.9 ft

D.12 ft

25.Find the volume of the pyramid below with a square base.

A.96 cm 3

B.120 cm3

C.144 cm3

D.180 cm3

26.Find the height of the cone if the volume is 60 m3.

A. m

B.5 m

C.8 m

D.30 m

ANSWERS – 2nd Semester Geometry Exam Review

Ch. 6

1.D2.B3.B4.B

5.A6.B7.B8.D

9.C10.E11.D12.A

13.D14.C15.C16.D

17.A18.B19.E20.A

21.C22.B23.A24.D

25.C26.A27.D28.B

29.D30.B31.D32.C

33.A34.C35.B36.D

37.B38.C

Ch. 8

1.C2.A3.B4.A

5.C6.C7.D8.A

9.D10.C11.C12.B

13.D14.C15.B16.A

17.D18.A19.C20.D

21.D22.C23.D24.B

25.C26.A27.B28.D

29.B30.C31.A

Ch. 9

1.C2.C3.A4.A

5.D6.B7.C8.B

9.D10.C11.C12.B

13.B14.C15.B16.A

17.D18.C19.B20.B

21.A22.B23.D24.C

25.B

Ch. 10

1.B2.B3.D4.B

5.D6.D7.A8.C

9.C10.D11.B12.B

13.A14.A15.B16.B

17.D18.A19.B20.C

21.D

Ch. 11

1.C2.A3.B4.B

5.C6.A7.C8.C

9.B10.D11.C12.D

13.D14.D15.B

Ch. 12

1.B2.B3.C4.B

5.D6.B7.D8.D

9.A10.D11.B12.D

13.D14.C15.C16.B

17.D18.B19.C20.A

21.C22.D23.D24.A

25.A26.B

March 23, 2004