Name: ___________________________________
Review Unit 3 Geo Honors
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1. In the following diagram, it is known that ABC and EF bisects AC at B. Which of the following cannot be
t
concluded from these givens?
(1) AB @ CB
(2) ÐDBE @ ÐCBE
(3) B is the midpoint of AC
(4) ÐDBC is supplementary to ÐDBA
2. Which of the following is not always true?
(1) vertical angles are congruent
(2) complements of congruent angles are congruent
(3) all right angles are congruent
(4) all obtuse angles are congruent
3. Alonzo knows that in the following diagram points A, B, C, and D are collinear and that AC = BD. He correctly
concludes that AB = CD . Which of the following would be the correct reason for this conclusion?
(1) a midpoint divides a segment into two
equal segments
(2) the whole is the sum of its parts
(3) the subtraction property of equality
(4) the addition property of equality
to
4. Tierra knows that right angles are congruent. To prove this she would need to use which important axiom
below?
(1) equals may be substituted for equals
(2) when equals are added to equals the sums are equal
(3) when equals are subtracted from equals the differences are equal
(4) the whole is the sum of its parts
5. In the following diagram it is given that DAFC is congruent to DDEB . Which of the following would justify
the statement that AC is congruent to DB ?
(1) corresponding parts of congruent triangles are
congruent
(2) the side angle side theorem
(3) the addition property of equality
(4) the whole is the sum of its parts
6. In which of the following diagrams is there not enough information shown to prove the given congruence
statement?
(1)
(3)
DABC @ DDBC
(2)
DACB @ DDEB
(4)
DABC @ DDBC
DABC @ DDBC
!!!"
!!!"
BD
7. In the diagram below, it is known that
bisects ÐABC , AD is perpendicular to BA , and CD is
!!!"
perpendicular to BC . Which of the following theorems could be used to prove that DDAB is congruent to
DDCB ?
(1) A.S.A.
(2) S.A.S.
(3) H.L.
(4) A.A.S.
i
8. Given that lines m and n shown below are parallel, which of the following pairs of numbered angles do not
need to be congruent?
(1) Ð2 and Ð3
(2) Ð3 and Ð5
(3) Ð1 and Ð2
(4) Ð4 and Ð5
9. In the diagram below, DE is parallel to GK and CA is perpendicular to BA . If mÐEAC = 35! then which
of the following is the measure of ÐABC ?
(1) 35!
(2) 45!
(3) 55!
35
359047180
xD
(4) 145!
10. Given the two lines m and n shown below cut by a transversal and the five numbered angles shown, which of
the following pieces of information would not be enough to conclude that m and n are parallel?
(1) Ð1 @ Ð4
(2) Ð3 and Ð4 are supplementary
(3) Ð2 @ Ð3
(4) Ð2 and Ð4 are supplementary
11. In DMNP it is given that NM is congruent to NP . Which of the following must be true?
if
(1) ÐPNM @ ÐPMN
N
(2) N lies on the perpendicular bisector of MP
(3) ÐMPN @ ÐMNP
(4) M lies on the perpendicular bisector of NP
12. In the diagram shown below, TR is perpendicular to RS , TW is perpendicular to WS , and TR is congruent
to TW . Which of the following would be used to show that DTRS @ DTWS ?
(1) S.S.S.
(2) S.A.S.
(3) A.A.S.
(4) H.L.
13. Which statement below is sufficient evidence to conclude that
DMNP is congruent to DXYZ ?
(1) MN = XY ; ÐM @ ÐX
St
(2) There is a sequence of rigid motions that maps the three side of DMNP to the
corresponding three sides of DXYZ . SSS
(3) ÐM @ ÐX ; ÐN @ ÐY ; ÐP @ ÐZ
(4) There is a sequence of rigid motions that maps point N to point Y, point P to point
AAA
Z, and NP to YZ .
S
14. Consider the diagram below in which the graphs of two triangles are shown. The vertices of DABC are at
A (1, 4.5) , B (1, 0.5) , and C ( 3, 0.5) . The vertices of DDEF are at D ( -1, 2 ) , E ( -1, - 2) , and F ( -3, - 2 ) .
(a) Use the properties of rigid motions to explain why
DABC is congruent to DDEF .
Top570pyaxis
(b) What triangle congruence theorem could be used to prove the two triangles are congruent? Explain.
3sidescankemeasveadtobe
95
all thesamemeasure
15. For triangle JKL and triangle PQR, it is known that JK @ PQ. Triangle JKL is guaranteed to be congruent to
triangle PQR if
P
J
c
i
g J torpoint
(2) There is a sequence of rigid motions that maps JL to PR and point
(1) ÐJ and ÐP are right angles.
P, and point L to point R.
(3) There is a sequence of rigid motions that maps ÐJ to ÐP and ÐK to ÐQ.
(4) Both triangles are acute triangles.
16. In the following diagram, BD is perpendicular to AC and bisects ÐABC . Which triangle congruence
theorem would be used to show that DADB is congruent to DCDB ? Justify your choice.
showevidenced
DB
DB
LBDCtLBDAarePight
LBDELBDA
LABDELLCBD
ABDI CBD
Given
Reflexiveproperty
Def.of 1
rightanglesarecongruent
Defofbisector
ASA
I
Y
E
17. In the diagram below, it is known that ÐQUS is congruent to ÐTUR . Prove that ÐQUR is congruent to
ÐSUT .
Y
Given
LRUSIRUS
LQURARUSCRUSTLSUT
LQURELSUT
ReflexiveProperty
Partitionaxioms
Subtractionaxioms
18. In the diagram below, lines m and n are parallel and AB is congruent to AC . Prove that Ð1 is congruent to
Ð2 .
Given
ABCis isosceles DefofIsosceles
23 24
LI 23 2224
LI 22
DefofIsosceles
Alt Intangles
Substitutions
y
19. In the diagram shown, HF bisects ÐEHG and EH @ GH .
Prove: EF @ GF
d
x
Given
FAITH
LEHFELGHF
EHFIGHF
EFIGF
I
ReflexiveProperty
DefofBisector
SAS
CPCTC
q
20. In the diagram shown AB and CE intersect at D such that D is the midpoint of AB . BC is parallel to AE .
Prove: D is also the midpoint of CE
r
show DEDE
e
LADEELBDC
Given
Vertical
angles
Defofmidpoint
LAILBLE Le AltIntangles
AD DB
AEDE BCD
CDI DE
Disthemidpointof
CE
ASA OPAAS
CPCTC
Defofmidpoint
n
1
L
I
9
21.In the diagram shown, NM and OQ are both congruent and parallel. Also, NR and OP are both
perpendicular to MP .
Prove: NR @ OP
i
Given
s
LNRMaLOPQ areright Defof 1
LNRMILOPQ
rightanglesare
LMILOQP
NARI OOP
Correspondingangles
AAS
CPCTC
NRIOP
E
LA135 70 180
LA 75
22. In the diagram shown, BD @ CD and BD bisects ÐABC . If
mÐADB = 70! as shown, then is DDAB isosceles? Justify your
response.
No
110
ODABisnotIsosceles
becauseitdoesn'thave 2
1
3535
35C
23. In quadrilateral EFGH shown below, both pairs of opposite sides are congruent.
Prove: EF is parallel to HG show
2 13
1
2
(Hint: Draw in diagonal EG )
EFFHG EH FG
EGIEG
Given
ReflexiveProperty
EGHIGEF
22 23
SSS
EFIIta
Altintanglesarecongevent
CPCTC
I
34