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Adv Geometry Term 1 Exam Review
l.
Name
f\
2. IfEbisects ZFGH,mZFGK=4x-12,
of QRifRis
between Q and T, QT : -4c ,
QR: 3c +29 , andRT: -2c - 4z
Findcandthemeasure
and m/-KGH =2x1-6 findx and nZFGH.
X=9
n- -q,
LtreH -- L+6"
*__;
3.
\./
A cylinder-shaped jar contains 30 cm' of water when the jar is frlled to the top.
The area of the base of the cylinder is 10cm' . What is the height of the jar?
The formula for the volume of a cvlinder is V : nr2h .
r-)
y1
is a trapezoid with H(5,4), I(I0, -2),
J(-8, -2), and K(-3,4). Find the coordinates of
the image of Flunder the translation
(x,y) -+ (x - 5,y + 6).
4. HIJK
H',a
5.
Cl,zt
Find the reflection of the point A(5, -2)
across the liney : x.
A'?A.P)
(O r to)
6. Name the image of C(4,6) under a rotation
90" counterclockwise about the
=J
7.
origin.
Make a conjecture given that
R is the midpoint of pS.
QRgRS
C' Cto,4)
8. Identify the converse of the statement If a triangle
is
lf a *-ianale
r)
has 3 non-congruent sides, then
ac/Ll?r1e-ihm i+ Vws
it is scalene.
3 non- bnq
r)
9. Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
Given: points A,
B,
and
Vale
C
e
Conjecture: A, B, and C are colinear.
g
A
.c
5\Aes.
Adv Geometry Term 1 Exam Review
10.
In the figure, ABIICD ,
mlE:
x,
mlD =52,
\= 3B
I
Name
and wIABD = y
5= 14O
l. Given all b and ml3 = 2x - 15
andml5:45, find ml6.
-12. Find x and y.
12.
containing (-2,16) and (3, 6)?
fl
r
6
L(o =
Which is an equation of the line
r-\
l^==o\X+ld
U
IVO
13. In the figure below, lines a & b are parallel. Lines c & d intersect at pointX.
Is the following statement valid?
lPxQ=
IRXS by the Corresponding Angles Postulate
Nol- Va-\ iC
14. Triangle FJH is an equilateral triangle.
Findx
andy.
H
8v
X*B
-
15.
is isosceles afi AE = FC
Which theorem or postulate
If LABC
4)"
U=B
16. zC isanaltitude,
ICW =1lx+38,
and ZI4rZC = 15x
.
Find
mlWC.
17. Find the measures of an interior angle
and an exterior angle for a regular
hexagon.
lrr_f
Ex*
: t\o
t (o0
,
Adv Geometry Term 1 Exam Review Name
18.
Quadrilateral ABCD is a rectangle.
If AC = I lx - 5 and DG = 2x +I5. find BD.
Find x and y so that this quadrilateral
is a parallelogram.
19.
x=5
9D= bo
20. What
X=l?
is the value of x?
X- lo
2r.
Given: Z is the midpoint of JM; JKll NM.
Prove: LIKL = LMNL
Proof:
Statements
a) Z is the midpoint of JM
rKll MN
Caive-n
b) JL=ML
de$
c) IJKL = IMNL
AIA
d) IJLK =
IMLN
e\ LIKL = LMNL
v
"l
Mid
erhcul
hA"
Po
Li
i
n*
()-f,(''
/
V=
2+
Adv Geometry Term
I Exam Review
Name
22.
THEOREM: Opposite sides of a parallelogram are congruent.
Given: PQRS is a parallelogram
Prove: PQ= RS and PR=QS
Proof:
Reasons
Statements
a) PO
b)
39 iz a" ?a.ra-ll.
FRttQs, FOtt
a) Q1v ?.n
D
6el ol 4'ra-
Lli LZ tL?= L+ C)AIA
d)ffi4m
il ret1zY\v"cc)
E)
APQRgASNQ
oEgRE
e)
ASA
D
SVITC
Q?z*
23.
THEOREM: If rwo parallel lines are cut by a tra.nsversal, then each pair
consecutive interior angles is supplementary.
Given: mlln, / is a transversal
Prove: ll and 12 are supplementary
13
and
14
are supplementary
Prooft
Statements
Reasons
a),,m.[[vt,L is Lraxe.
*' at i L3 arz livr Tair
a)
art- lin V.ia
c) al1.L? a-rz suf?
lZ,t L* art 5v??
^', La q
d) et
a.f
t*
and LAe- Lz
"
e) Ll c. L?, ur L bu7?
La e. t* a).e- 60 P?
Siven
D deP
c)
ol lin. Wir
lin. Pairs arL
d) AIA
e)
a{Q.
S ubs't-r
z
tufio n
9U PP.
of
Adv Geometrv Term 1 Exam Review Name
Draw and label a figure on your answer sheet that can be used in a coordinate proof to prove the theorem
below. Then provide the Given and Prove statements for the proof.
24. THEOREM: The diagonals of a parallelogram bisect each
Gtve-n'.
?rove'
AAco is a ?&10"116\o3
" AC
C
other.
ca'ry1
Da€L(k5EA
Write a complete two-column proof of the theorem below using the frgure provided.
25. THEOREM: If nuo angles are vertical angles, then they are congruent.
Proof:
Statements
Reasons
D
a) 6lvo*t
"jffffi1
HtTiuf
t1?. L7 ara- lin p4i7
D) L+7
tz *ro lin pir
L7= l3O
n\
v' 2l+
LZ+LL: IBO
olt+LV--LV+A
del of lin pair
c) €v?? le-vlen* l*ttnreu
b)
lvbqhtufi on
0ooM*cAon
d)
e) Ll=- L
Write a complete coordinate proof of the theorem below using the figure provided.
26. THEOREM: If a line segment joins the midpoints of two
then it is parallel to the third side.
Midvoinr'
triangle,
r
K t(ry,+)--
c=-+q-\=
ffi -t (cb
\ Ft:J-
S\op.: N=
9c
-.L2-
b_
a(
?t
sides of a
=
-U
BIC
+lopt-s ora' 1-l^& s&rfie)
XY
ll-sr