17
M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 2 2 2 1 2 1 d x x y y 1 2 1 2 , midpoint 2 2 x x y y A bh 1 2 A bh 2 A r 2 C r The following formulas will NOT be given on the exam, but you will need to know them: sum of interior s 2 180 of an -gon n n sum of exterior s 360 of any polygon 2 1 2 1 slope = y y x x y mx b y k m x h Semester 1 Vocabulary acute angle corresponding parts line of symmetry rotation acute triangle corresponding sides line segment rotational symmetry adjacent angles counterexample midpoint scalene triangle alternate exterior angles decagon n-gon segment bisector alternate interior angles degree nonagon side angle diagonal obtuse angle skew lines angle bisector distance obtuse triangle slope angle of rotation edge octagon slope-intercept form area equiangular polygon opposite rays space base equiangular triangle parallel lines sphere base angles equidistant parallel planes statement between equilateral polygon perimeter supplementary angles center of rotation equilateral triangle pentagon surface area circumference exterior perpendicular symmetry collinear exterior angle plane theorem complementary angles heptagon point translation concave hexagon point-slope form transversal conclusion hypothesis polygon triangle conditional statement included angle proof vertex angle congruent included side quadrilateral vertex of an angle congruent triangles isosceles triangle ray vertex of a polygon consecutive interior angles interior reason vertical angles contrapositive intersection reflection x-intercept converse inverse regular polygon y-intercept convex line remote interior angles coplanar linear pair right angle corresponding angles line of reflection right triangle

M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

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Page 1: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

1

M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam:

2 2

2 1 2 1d x x y y           1 2 1 2, midpoint2 2

x x y y

 

A bh    1

2A bh     2A r       2C r  

The following formulas will NOT be given on the exam, but you will need to know them:

sum of interior s

2 180of an -gon

nn

   

sum of exterior s360

of any polygon

 

 

2 1

2 1

slope = y y

x x

y mx b y k m x h

Semester 1 Vocabulary acute angle corresponding parts line of symmetry rotation acute triangle corresponding sides line segment rotational symmetry adjacent angles counterexample midpoint scalene triangle alternate exterior angles decagon n-gon segment bisector alternate interior angles degree nonagon side angle diagonal obtuse angle skew lines angle bisector distance obtuse triangle slope angle of rotation edge octagon slope-intercept form area equiangular polygon opposite rays space base equiangular triangle parallel lines sphere base angles equidistant parallel planes statement between equilateral polygon perimeter supplementary angles center of rotation equilateral triangle pentagon surface area circumference exterior perpendicular symmetry collinear exterior angle plane theorem complementary angles heptagon point translation concave hexagon point-slope form transversal conclusion hypothesis polygon triangle conditional statement included angle proof vertex angle congruent included side quadrilateral vertex of an angle congruent triangles isosceles triangle ray vertex of a polygon consecutive interior angles interior reason vertical angles contrapositive intersection reflection x-intercept converse inverse regular polygon y-intercept convex line remote interior angles coplanar linear pair right angle corresponding angles line of reflection right triangle

Page 2: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

#1-11: True or false? If false, replace the underlined word or phrase to make a true sentence. 1. Two lines are perpendicular if they intersect to form a right angle. 2. Two angles are congruent if their measures have a sum of 90. 3. If two rays intersect at a common endpoint, a plane is formed. 4. A theorem is a statement that describes a fundamental relationship between the basic terms of geometry.

For #5-7, refer to the figure at right. 5. 4 and 5 are corresponding angles.

6. Given r || t, then consecutive interior angles 4 and 6 are supplementary. 7. Line p is a transversal since it intersects one or more lines in a plane at different points. 8. A triangle that is equilateral is also called a(n) acute triangle. 9. A(n) obtuse triangle has exactly one obtuse angle. 10. A reflection is a transformation that moves all points of a figure the same distance in the same direction. 11. When a figure can be folded so that the two halves match exactly, the fold is called a line of reflection. #12-17: Choose the correct term to complete each sentence. 12. Vertical angles are two (nonadjacent or collinear) angles formed by two intersecting lines. 13. The (midpoint or angle bisector) divides a line segment into two congruent segments. 14. When a linear equation is written in the form y = mx + b, m is the (transversal, slope) of the line and b is

the y-intercept. 15. (Corresponding angles, Interior angles) are located between the lines cut by a transversal. 16. An (interior or exterior) angle is formed by one side of a triangle and the extension of another side. 17. The SAS Postulate involves two corresponding sides and the (exterior angle or included angle) they form.

Page 3: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

#18-30: Choose from the terms on page 1 to complete each sentence. 18. A(n) ? divides an angle into two congruent angles. 19. Two angles are ? if their measures have a sum of 180. 20. Two angles that lie in the same plane are called ? if they share a common side and a common

vertex. 21. The statement immediately following the word if is called the ____? ___ of an if-then statement. 22. The statement immediately following the word then is called the ____? of an if-then statement.

23. The equation 56 2

8y x is in ? form.

24. If two ? are cut by a transversal, then each pair of alternate interior angles is congruent. 25. A(n) ? organizes a series of statements in logical order, starting with the given statements. 26. A triangle that has one 90° angle is called a(n) ? . 27. The ASA postulate involves two corresponding angles and their corresponding ? . 28. The ? is formed by the congruent legs of an isosceles triangle. 29. A transformation representing a flip of a figure is called a(n) ? . 30. A(n) ? is a transformation that turns every point of a pre-image through a specified angle

and direction about a fixed point. #31-34: Use the figure at the right. 31. What is another name for line ? 32. Name three points on plane P. 33. Name the intersection of planes P and N. 34. Name three non-coplanar points.

Page 4: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

35. If the figure at right is not necessarily drawn to scale:

a. State one thing we CAN assume from the diagram:

b. State one thing we CANNOT assume from the diagram:

36. What is the length of AB?

37. Find the length of DE if D is between points C and E, CD = 6.5 cm, and CE = 13.8 cm.

38. Write an equation and solve. Then find the length of XZ shown at right. 39. A square has a side length of 2.3 ft. What is the area of the square? Include units with your answer. 40. A circle has a circumference of 6 cm. Find the diameter of the circle. Include units with your answer. #41-43: Use the coordinate grid given at right. 41. Find the distance between A and B. Express your answer in simplest

radical form.

42. Find the coordinates of the midpoint of CD.

Page 5: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

43. Find the coordinates of a point E if C is the midpoint of AE. 44. The vertices of a triangle are 0,0P , 8,6Q , and 3, 4R . What is the perimeter of this triangle?

45. Find the value of x and y in the figure at right if UV bisects TW and UV = 40. 46. Use a protractor to measure PQR . Then classify PQR as right, acute, or obtuse.

#47-48: In the figure, EA

and EB

are opposite rays, and EC

bisects FEG . 47. Find the value of x if 82m FEG , and 5 11m FEC x .

48. If 16 10m AED y , find the value of y so that ED AB . 49. Find x, y, m 1 , and m 2 in the figure at right.

Page 6: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

#50-51: Use the polygons at the right. 50. Name polygon ABCDEF by its sides. Then classify it as

convex or concave and regular or not regular. 51. Find the length of each side of polygon RST. 52. Two angles, 1 and 2 , are supplementary. Angle 1 is an acute angle. What type of angle is 2 ? 53. Write an equation, and solve: The length of a rectangle is 3 more than twice its width. Find the area of the

rectangle if its perimeter is 30 cm. 54. What is the perimeter of a regular hexagon if one side is 9 cm long? 55. Find the measure of one interior angle of a regular heptagon. 56. The measure of one exterior angle of a regular polygon is 15°. How many sides does the polygon have? 57. Find the value of x in the figure at right.

58. Give a counterexample to show this statement is false: If XY = YZ, then Y is a midpoint of XZ.

Page 7: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

59. Write the following statement in if-then form: All dogs have four feet. 60. Identify the hypothesis of the statement: If you live in Chicago, then you live in Illinois. 61. Write the converse of the statement: If two lines are perpendicular to the same line, then they are

parallel. 62. Write the inverse of the statement: If today is January 1, then it is New Year’s Day. 63. Write the contrapositive of the statement: If today is New Year’s Day, then school is closed. 64. Complete the proof by supplying the missing information:

If 2 7 4x , then 11

2x .

Statements Reasons 1. 2. 2 7 7 4 7x 3. 4.

5. 11

2x

1. Given 2. 3. Simplify (or substitution) 4. 5. Simplify (or substitution)

65. If 1 50m x and 2 3 20m x , find 1m .

Page 8: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

66. Complete the proof.

Given: AC bisects BAD . AC bisects BCD . 1 2 Prove: 3 4 Statements Reasons

1. AC bisects BAD . AC bisects BCD. 1 2

2. ____ ____ and ____ ____ 3. 3 4

1. Given 2. 3.

#67-72: Give the reason that justifies each statement.

67. If M is the midpoint of AB, then AM MB . 68. If A B and B C , then A C . 69. If 90m A m B and 20m B , then 20 90m A . 70. If X and Y are complementary, Z and Q are complementary, and X Z , then Y Q . 71. If PR QT , then PR = QT. 72. In the diagram at right, AB + BC = AC. #73-74: Refer to the figure at right. 73. Identify the intersection of plane SVX and plane STU.

74. Name a segment skew to WY .

Page 9: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

#75-79: Refer to the figure at right.

Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

75. 2 and 12 76. 3 and 5 77. 7 and 15 78. If m n , and 8 86m , find 13m . 79. Find the values of x and y if m n , 4 6 5m x , 10 5 8m x , and 9 3 10m y . #80-82: Find the slope of the line that passes through the given points. Express answers as integers or fractions in simplest form. 80. 10, 4V , 5, 5W 81. 2, 9A , 2, 15C 82. 6,14G , 3,9L

#83-85: Find the slopes of CS

and KP

, and determine whether the lines are parallel, perpendicular, or neither. 83. 1, 12 , 5, 4 , 1,9 , 6, 6C S K P

84. 5, 6 , 3, 2 , 2,10 , 1, 4C S K P

85. 6, 7 , 3, 5 , 3,3 , 9, 7C S K P

Page 10: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

#86- 86. s #89-whic 89. 90. 91. m 92. F 93. U

a

b

c

d

e

f

-88: Write a

slope = 9 ,

-91: Given tch lines, if a

1 2

D A B E

m AD E m

Find the valu

Use the grid

a. Draw segm

b. Find the m

c. Find the sl

d. Find the sl

e. Write an ein point-sl

f. Graph you

an equation

y-intercept =

the followingany, are par

E B C

18m BED

ue of x so tha

to answer th

ment AB wit

midpoint M o

lope of AB.

lope of a line

equation for lope form.

ur equation fr

M2 

for the line

= 3 87

g informatiallel. State t

80

at a b .

he following

th 1,8A an

of AB. Labe

e perpendicu

the perpend

rom part (e)

GEOMETRY SE

e that satisfi

. slope = 3, c

on and the fthe reason t

g:

nd 5, 4B

l M on the g

ular to AB.

dicular bisect

on the grid a

EMESTER 1 REV

10 

es the given

contains (–1

figure at rigthat justifie

4 .

graph.

tor of AB 

above.

VIEW PACKET

n conditions

, 5) 8

ght, determs your answ

s.

88. x-intercep

mine wer.

pt is 3, y-inteercept is 1

Page 11: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

g

94. G

a

b

c

d

e

f

g

95. G

m

a

g. Use algebrGiven the gr

a. Find the

b. Find the yLabel thi

c. Find the

d. Find the and havin

e. Graph yothis line p

f. Use subs

g. Find the in simple

Given the gr

m: –2 –y x

a. Find the

ra to write yaph of the li

slope of the

y-intercept ois point A in

slope of any

equation of ng the same

our perpendip.

stitution to fi

distance betest radical fo

aph of the li

–5 :

slope of the

M2 

your equationnes : y x

lines.

of line , anthe graph.

y line perpen

a line perpeny-intercept a

icular line in

ind the point

tween the paorm.

nes : –y

lines.

GEOMETRY SE

n from part (6x and m

nd write it as

ndicular to

ndicular to tas .

n the same gr

t of intersect

arallel lines b

–2 10x an

EMESTER 1 REV

11 

(e) in slope-i: 8y x :

s a point.

and m.

o and m

rid. Label

tion of m and

by finding th

d

VIEW PACKET

intercept for

d p. Label th

he distance b

rm.

his point B in

between A an

n the graph.

nd B. Write y

your answer

 

Page 12: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

b

c

d

e

f

g

96. S

a

b

b. Find the y

c. Find the

d. Find the

e. Graph yo

f. Use subs

g. Find the

Suppose line 0, 1 and

a. Graph an

b. Find the

y-intercept o

slope of any

equation of

our perpendi

stitution to fi

distance bet

e passes th 3, 5 :

nd label line

slope of .

M2 

of line , an

y line perpen

a line perpen

icular line in

ind the point

tween the pa

hrough the f

.

GEOMETRY SE

nd write it as

ndicular to

ndicular to t

n the same gr

t of intersect

arallel lines. W

following po

EMESTER 1 REV

12 

s a point. Lab

and m.

o and m a

rid. Label thi

tion of m and

Write your a

oints

VIEW PACKET

abel this poin

and having t

is line p.

d p. Label th

answer in sim

nt A in the gr

the same y-in

his point B in

mplest radic

raph.

ntercept as

n the graph.

al form.

.

Page 13: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

c

d

e

f

g

h 97. U

d 98. F

c. Write an

d. Find the

e. Write the

f. Graph th

g. Use subs

h. Use the d

Use a protracdegree and n

Find x, AB, B

equation for

slope of a lin

e equation of

e line from p

stitution to fi

distance form

ctor and rulenearest cm.

BC, and AC i

M2 

r .

ne perpendic

f a line perpe

part (e) in th

ind the point

mula to calcu

er to classify

if A B C is

GEOMETRY SE

cular to .

endicular to

he same grid.

t of intersect

ulate the dist

y the triangle

equilateral.

EMESTER 1 REV

13 

and passi

. Label this l

tion of lines

tance betwee

e by its angle

VIEW PACKET

ing through

line k.

k and . La

en and P.

es and sides.

2,5P .

abel this poin

Round mea

nt Q in the g

asurements to

graph.

o the nearestt

Page 14: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

14 

WH 

S

P S 

R Q

99. Use the distance formula to find the lengths of the sides of E F G if its vertices are 3,3E , 1, 1F , and

3, 4G . Then classify the triangle by its sides.

100. Use the figure to find the measure of each numbered angle. 101. Write two different congruence statements for the triangles shown at right. ________ ________ ________ ________ #102-103: If the given postulate proves the two triangles are congruent, which additional parts of each pair of triangles should be shown congruent?

102. AAS 103. ASA

_______ ________ _______ _______

104. In the figure at right, IH bisects W IS . For each pair of triangles: (a) Are they congruent? (b) If yes, write the triangle congruency statement, and (c) give the postulate that makes them congruent.

a. Write a triangle congruence statement:

D C 

B A

Page 15: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

M2 GEOMETRY SEMESTER 1 REVIEW PACKET 

15 

________ ________

b. Explain why these two triangles are congruent. 105. Write a two column proof.

Given: RS TS , and V is the midpoint of RT Prove: RSV TSV 106. Write a two column proof on separate paper.

Given: D F , and bisects GE DEF

Prove: DG FG

107. KLM is isosceles, and 1 2 .

a. Explain why LK P LM N .

b. Name the reason that could be used to prove LK P LM N . Choose from SSS, SAS, ASA, and AAS.

108. Find 1m .

V

R

T

S

D

E

F

G

Page 16: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

109. 110.

111.

112.

Find the va

Write the co

Graph A B

graph the im

Graph the im

4,5X af

lue of x.

oordinates o

B C with ver

mage of A B

mage of WX

fter the trans

M2 

of the image

rtices 4, 4A

B C reflected

X with 7W

slation 4x

GEOMETRY SE

of 2,5P

, 3, 2B ,

d in the y-ax

7,1 and

4, 3y .

EMESTER 1 REV

16 

reflected in

and 1,C

xis.

113.

VIEW PACKET

the line y =

1 . Then

. Graph the i

1,5B af

origin.

2.

image of ABfter a rotatio

B with 3A

on of 90 abo

3,1 and

out the

Page 17: M2 GEOMETRY REVIEW FOR MIDTERM EXAM...M2 GEOMETRY SEMESTER 1 REVIEW PACKET 1 M2 GEOMETRY REVIEW FOR MIDTERM EXAM The following reference formulas will be provided on the exam: 22 dxx

114.

t

Find the co

3,1L , M

90 about ththe x-axis.

ordinates of

1, 6 , and

he origin and

M2 

f L′′ if LMN

3, 2N is

d then reflect

GEOMETRY SE

N with

s rotated

ted over

EMESTER 1 REV

17 

115.

VIEW PACKET

. A B C wit

and 3,C

What are th

th vertices A

1 is rotated

he coordinat

4, 4A , B

d 180 about

tes of triangl

1, 2B ,

t the origin.

le A′B′C′?