GEOMETRY • FINAL REVIEW • SOLVE THESE ON SEPARATE SHEETS OF PAPER!!! • THE FIRST TWO PAGES HAVE THE MOST IMPORTANT TOPICS, AS THEY’LL BE OPEN ENDED QUESTIONS 20. Congruence and Parallelogram Properties In the diagram, PQRS is a parallelogram. A) Draw in a diagonal of PQRS. B) Name the two triangles created from the diagonal you drew in part A. ____________ and ___________ Identify all congruent segments and all congruent angles in these two triangles. Congruent Segments: Congruent Angles: ________ ≅ _________ ________ ≅ _________ ________ ≅ _________ ________ ≅ _________ ________ ≅ _________ ________ ≅ _________ C) If the area of one of the triangles was 12 cm 2 , then what would be the area of the other triangle? Explain your reasoning. 16. Similarity and Proportions A) Explain why ∆!"# ≅ ∆!"#. B) Explain why ! ! = ! ! C) Explain why !" !" = !" !" If angles B and Q are right angles 13. Triangle Sum Theorem and AlternateTInterior Angles Theorem Prove the triangle sum theorem with auxiliary line drawn in and alt interior angles congruent A) m<5 = m<_______ because they are ___________________ m<_______ = m<2 because they are ___________________ B) m<3 + m<_____ + m<2 = 180 because they are ___________________ m<1 + m<4 + m<5 = ______ because _______________________________ C) Use the diagram above to informally prove (explain) that the interior angles of a triangle are supplementary. R S
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GEOMETRY(•(FINAL(REVIEW(•(SOLVE(THESE(ON(SEPARATE(SHEETS(OF(PAPER!!!(•(THE(FIRST(TWO(PAGES(HAVE(THE(MOST(IMPORTANT(TOPICS,(AS(THEY’LL(BE(OPEN(ENDED(QUESTIONS((
20.(Congruence(and(Parallelogram(Properties(In#the#diagram,#PQRS#is#a#parallelogram.(A)((Draw#in#a#diagonal#of##PQRS.#(((B)((Name#the#two#triangles#created#from#the#diagonal#you#drew#in#part#A.##____________#and#___________#Identify#all#congruent#segments#and#all#congruent#angles#in#these#two#triangles.#
Congruent#Segments:## # # Congruent#Angles:#________#≅#_________# # # # ________#≅#_________#________#≅#_________# # # # ________#≅#_________#________#≅#_________# # # # ________#≅#_________#
C)(#If#the#area#of#one#of#the#triangles#was#12#cm2,#then#what#would#be#the#area#of#the#other#triangle?##Explain#your#reasoning.#16.(Similarity(and(Proportions(
A)(Explain#why#∆!"# ≅ ∆!"#.# # # B)((Explain#why#!! = !
!!(
(
( (
C) Explain#why#!"!" = !
!"!"##
If#angles#B#and#Q#are#right#angles#(13.(Triangle(Sum(Theorem(and(AlternateTInterior(Angles(Theorem(Prove#the#triangle#sum#theorem#with#auxiliary#line#drawn#in#and#alt#interior#angles#congruent#
#A) #m<5##=#m<_______##
because#they#are#___________________##
#####m<_______#=#m<2#####because#they#are#___________________#
#B) #m<3#+#m<_____#+#m<2#=#180#
because#they#are#___________________##
## m<1#+#m<4#+#m<5#=#______## ####because#_______________________________#
#C)##Use#the#diagram#above#to#informally#prove#(explain)#that#the#interior#angles#of#a#triangle#are####supplementary.#
R#S##
19.(Similarity( ( Are#these#triangles#similar?##If#so,#write#a#similarity#statement.#
A)(( ( ( ( ( B)( ( ( ( ( C)(
#
(
(
(##18.(Similarity(and(Proportions(in(Real(Life.(Draw(a(diagram(to(help(answer(the(following:(A)(( ( ( ( ( ( ( ( ( ( (( ( ( ( ( ( ( ( C)(((B)(
(15.(Trig(and(45T45T90(Triangles(
A) (
B) (
C) (3.(Dilations(and(similarity(of(dimensions(
A)# (
B)# (
C)# (#
11.( When(two(parallel(lines(are(cut(by(a(transversal…( ( ( (a.# # # # # # # # # # # # # b.#
#######cVd.#Find#x#in#the#following#diagrams#in#order#for#the#lines#to#be#parallel#
## #1.Volume(and(Density(( A)#What#is#the#mass#of#ethyl#alcohol#that#fills#a#200#mL#container?#The#density#of#ethyl#alcohol#is#
0.789#g/mL.#(B)##A#rectangular#solid#of#unknown#density#is#5#meters#long,#2#meters#high,#and#4#meters#wide.#The#mass#of#this#solid#is#300#grams.#Given#this#information#for#this#homogeneous#material,#calculate#the#density.## # # # # # # # # # # ## C)##A#sample#of#iron#has#the#dimensions#of#2#cm#x#3#cm#x#2#cm.#What#is#the#mass#if#the#density#is### 7.83g/cm^3?#((4.(FIND(THE(PERIMETER(OF(TRIANGLES:(A# # # # # B# # # # # C# # #
#(
(5x#+#10)#
Name ________________________________________ Date ___________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Parallel and Perpendicular Lines Chapter Test Form B
Circle the best answer.
Use the figure for Exercises 1 and 2.
1. Classify EH and .DH
A skew segments
B parallel segments
C perpendicular segments
D parallel planes
2. How many segments are skew to AE ?
F 1 H 3
G 2 J 4
Use the figure for Exercises 3 and 4.
3. Which are alternate exterior angles?
A 1 and 3 C 3 and 6
B 1 and 8 D 6 and 7
4. Which statement is true?
F 1 and 2 are alternate interior angles.
G 1 and 3 are corresponding angles.
H 3 and 6 are alternate exterior
angles.
J 3 and 7 are same-side interior
angles.
5. Which correctly completes the sentence?
If two parallel lines are cut by a transversal,
then the two pairs of same-side interior
angles are _________.
A supplementary
B complementary
C corresponding
D congruent
6. What type of angle is 1?
F acute H obtuse
G right J straight
7. Given ,HJJG HJJGRS QP|| what is the value of x?
A 6 C 72
B 9 D 108
Use the figure for Exercises 8 and 9.
8. Which information proves that r || s?
F 1 3 H 4 6
G 4 5 J 5 6
9. If m 3 (4x 20) and
m 5 (6x 10) , what value
of x proves that r || s?
A 5 C 40
B 15 D 100
10. If a transversal is perpendicular to one of
two parallel lines, how many different
angle measures are formed?
F 1 H 4
G 3 J 8
Name ________________________________________ Date ___________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Parallel and Perpendicular Lines Chapter Test Form A continued
11. Which segment’s length gives the distance from G to line ?
A GF B GE
12. Which inequality is correct?
A x 23 B x 20
13. If 1 2 and 4 is a right angle, which postulate or theorem is used to prove m || n?
A Alt. Int. Thm. B 2 lines to same line 2 lines are || C Corr. Post. D Vert. Thm.
14. What type of slope does the line have?
A positive C zero B negative D undefined
15. What is the slope of the line through (3, 6) and (4, 2)?
A 4 C 87
B 14
D 4
16. Given a line with a slope of 2, what is the slope of a line parallel to the given line?
A 2 C 12
B 12
D 2
17. Which equation is in slope-intercept form?
A 2 93
y x
B 22 ( 6)3
y x
18. A line parallel to the x-axis could contain which point? A (0, 2) B (2, 0)
19. Which line is perpendicular to y 2x 4?
A y 2x 6 B 1 72
y x
20. What is the equation of the line through ( 1, 8) and (4, 18)?
A 1 102
y x C y 2x 10
B x 2y 10 D 2x y 10
Chapter
x
49
Chapter
3
49
CS10_G_MEAR710334_C03MCCT.indd 49 405011 12:08:41 PM
2.(Similarity(A.# Determine#whether#the#triangles#are#similar.#EXPLAIN#WHY/HOW#or#WHY#NOT.##If#they#ARE#similar,#write#a#similarity#statement.#If#possible,#find#the#scale#factor.#
2A1 ## # # 2A2 (#B.# If#trail#EFGH#is#similar#in#shape#to#trail#ABCD,#what#is#the#distance#Malik#would#have#to#run#to#complete#one#lap#around#trail#EFGH?#(
((C.##Solve#for#x#and#y.##(#######D.# Quadrilateral#EFGH#is#similar#to#quadrilateral#JKLM.##Solve#for#x#.###
#(########
y#
5.5#y#
12.5#
5.(TRANSFORMATIONS(AND(CONGRUENCE(A)##Rotate#the#figure#90#degrees#clockwise#about#the#origin.##Then#translate#down#3.#
##C)##Out#of#the#two#series#of#transformation#which#of#the#following#creates#an#image#that#is#not#congruent#to#its#pre#image?##Explain.##6.# Midpoint#A)#Find#the#midpoint#of#the#line#segment#AB.# # B)# ############C)#What#is#the#midpoint#of#the#straight#line#segment#joining#the#points#(V2,#5)#and#(6,#V1)?###7.(Rotations(and(congruence(A)#Explain#in#terms#of#transformations## # # B)#Explain#in#terms#of#transformations#how#<D#is##how#<J#is#congruent#to#<F?# # # # # congruent#to#<A’?# # #############(((
B)##Reflect#the#triangle#over#the#yVaxis#and#dilate#with#scale#factor#½#about#the#origin.##
8.( The(following(are(parallelograms.(Find(x(and(y.(
a. # # # b.# # (
c.# #9.( Circles/(Equations#a.## Determine#whether#the#point#(V1,V3)#lies#on#the#circle#centered#at#the#origin#whose#radius#is#3.#b.# Does#the#point#(V6,V5)#lie#on#the#circle#centered#at#(3,8)#that#contains#the#point#(3,1)?#
c.# Does#the#point#(3,2)#lie#on#the#circle#that#has#the#equation# x −3( )2 + y+ 4( )2 = 36 #d.# #Prove#that#the#point#(6,1)#lies#on#the#circle#with#center#(6,V2)#with#radius#3#10.( Area(of(Sectors(and(Arc(Lengths(of(Circles(A.#
#B)#An#8#ftVbyV10#ft.#floating#dock#is#anchored#in#the#middle#of#a#pond.##The#bow#of#a#canoe#is#tied#to#a#corner#of#the#dock#with#a#10Vft#rope#as#shown#in#the#picture#below.########C.#Use#circle#R#to#find#BOTH#the#arc#lengths#and#the#area#enclosed#by#the#following#arcs:### # # # •VT# # # •VTU# # # •USV# ########
Prentice Hall Geometry • Teaching ResourcesCopyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
17
Name Class Date
6-2 Standardized Test Prep
Properties of Parallelograms
Multiple ChoiceFor Exercises 1–5, choose the correct letter.
1. In ~ABCD, m/A 5 53. What is m/C?
37 53 127 307
2. What is the value of x in ~QRST?
16 8
12 4
3. What is the value of y in ~LMNO?
4 12
6 24
4. What is m/1 in this parallelogram?
20 80
60 100
5. What is m/2 in this parallelogram?
115 15
50 2
Extended Response 6. Figure ABCD is a parallelogram. What are four geometric attributes
you know because ABCD is a parallelogram?
T
Q R
S
8 123x 2x
L M
NO
y 6x
3x
y 12
1 5m
(3m 20)
115
1
250
A B
CD125°#
To#plant#flowers#partially#around#a#tree#in#front#a#house…###•#How#much#area#would#the#flowers#need#to#cover?##•#I#would#also#like#to#put#a#layer#of#brick#around#the#edge#of#the#flowers#along#the#arc.##How#much#length#would#the#brick#cover?##
What#is#the#area#of#the#circle#that#the#canoe#can#travel?###What#is#the#perimeter#the#bow#of#the#boat#can#cover?##
12.A)(((Which line is parallel to = +y x1 52
? a. 2y = x + 7 b.y = −2x + 5 c. 2y = x + 10 d. y = 2x + 10
B)((Which#line#is#parallel#to#3y#=#x#+#9?#a.##x#+#3y#=#2# # b.##V2x#+#6y#=#8# c.#–x#+#y#=#6# # d.##x#+#y#=#9#
C)((Which#line#is#parallel#to##4x#–#5y#=#20?## a.##V4x#+5y#=#V20# b.#2x#–#10y#=#40# c.#4x#+#5y#=#V20# d.#5x#–#4y#=#20# 14##
C)(sin(x(=(cos________(( (#17#Similarity#and#Dilations#A)( ( ( ( ( ( ( ( B)(
(((((((
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