Take Home #1
Name:
1.
Date:
The vertices of ^JKL have coordinates
J(5; 1), K( 2; 3), and L( 4; 1). Under which
transformation is the image ^J 0 K 0 L0 not
congruent to ^JKL?
3.
In the diagram below, congruent
and 3 are drawn.
gures 1, 2,
(1) a translation of two units to the right and
two units down
(2) a counterclockwise rotation of 180 degrees
around the origin
(3) a re ection over the x-axis
(4) a dilation with a scale factor of 2 and
centered at the origin
Which sequence of transformations maps
gure 1 onto gure 2 and then gure 2 onto
gure 3?
(1) a re ection followed by a translation
(2) a rotation followed by a translation
(3) a translation followed by a re ection
2.
Which regular polygon has a minimum rotation
of 45 to carry the polygon onto itself?
(1) octagon
(3) hexagon
(2) decagon
(4) pentagon
(4) a translation followed by a rotation
page 1
4.
6.
Quadrilateral ABCD has diagonals AC and BD.
Which information is not su cient to prove
ABCD is a parallelogram?
Which statement is su cient evidence that
^ DEF is congruent to ^ABC?
(1) AC and BD bisect each other.
(2) AB = CD and BC = AD
(3) AB = CD and AB k CD
(4) AB = CD and BC k AD
(1) AB = DE and BC = EF
(2) OD = OA, OB = OE, OC = OF
(3) There is a sequence of rigid motions that
maps AB onto DE, BC onto EF, and AC
onto DF.
(4) There is a sequence of rigid motions that
maps point A onto point D, AB onto DE,
and OB onto OE.
5.
Steve drew line segments ABCD, EFG, BF,
and CF as shown in the diagram below.
Scalene ^BFC is formed.
Which statement will allow Steve to prove
ABCD k EFG?
(1) OCFG = OFCB
(3) OEFB = OCFB
(2) OABF = OBFC
(4) OCBF = OGFC
7.
A parallelogram must be a rectangle when its
(1) diagonals are perpendicular
(2) diagonals are congruent
(3) opposite sides are parallel
(4) opposite sides are congruent
page 2
Take Home #1
8.
If ^A0 B0 C0 is the image of ^ ABC, under
which transformation will the triangles not be
congruent?
10.
In the diagram below, a square is graphed in
the coordinate plane.
(1) re ection over the x-axis
(2) translation to the left 5 and down 4
(3) dilation centered at the origin with scale
factor 2
(4) rotation of 270 counterclockwise about the
origin
A re ection over which line does not carry the
square onto itself?
9.
In the diagram of parallelogram FRED shown
below, ED is extended to A, and AF is drawn
such that AF = DF.
(1) x = 5
(3) y = x
(2) y = 2
(4) x + y = 4
If mOR = 124 , what is mOAFD?
(1) 124
(2) 112
(3) 68
(4) 56
page 3
Take Home #1
11.
A sequence of transformations maps rectangle
ABCD onto rectangle A00 B00 C00 D00 , as shown in
the diagram below.
12.
Which sequence of transformations maps ABCD
onto A0 B0 C0 D0 and then maps A0 B0 C0 D0 onto
A00 B00 C00 D00 ?
(1) a re ection followed by a rotation
Given MN shown below, with M( 6; 1) and
N(3; 5), what is an equation of the line that
passes through point P(6; 1) and is parallel to
MN?
(1) y =
2
3x + 5
(3) y = 32 x + 7
(2) y =
2
3x
(4) y = 23 x
3
8
(2) a re ection followed by a translation
(3) a translation followed by a rotation
(4) a translation followed by a re ection
page 4
Take Home #1
13.
!
In the diagram below, FE bisects AC at B, and
!
GE bisects BD at C.
14.
In parallelogram QRST shown below, diagonal
TR is drawn, U and V are points on TS and
QR, respectively, and UV intersects TR at W.
Which statement is always true?
If mOS = 60 , mOSRT = 83 , and mOTWU = 35 ,
what is mOWVQ?
(1) AB = DC
(1) 37
(2) 60
(3) 72
(4) 83
(2) FB = EB
!
(3) BD bisects GE at C.
!
(4) AC bisects FE at B.
15.
Which transformation would result in the
perimeter of a triangle being di erent from the
perimeter of its image?
(1) (x; y) ! (y; x)
(2) (x; y) ! (x; y)
(3) (x; y) ! (4x; 4y)
(4) (x; y) ! (x + 2; y
page 5
5)
Take Home #1
16.
Triangle ABC and triangle DEF are graphed on
the set of axes below.
17.
The diagram below shows parallelogram LMNO
with diagonal LN, mOM = 118 , and
mOLNO = 22 .
Explain why mONLO is 40 degrees.
Which sequence of transformations maps
triangle ABC onto triangle DEF?
(1) a re ection over the x-axis followed by a
re ection over the y-axis
(2) a 180 rotation about the origin followed by
a re ection over the line y = x
(3) a 90 clockwise rotation about the origin
followed by a re ection over the y-axis
(4) a translation 8 units to the right and 1 unit
up followed by a 90 counterclockwise
rotation about the origin
page 6
Take Home #1
18.
In the diagram below, which single
transformation was used to map triangle A onto
triangle B?
19.
Quadrilateral ABCD is graphed on the set of
axes below.
When ABCD is rotated 90 in a counterclockwise
direction about the origin, its image is
quadrilateral A0 B0 C0 D0 . Is distance preserved
under this rotation, and which coordinates are
correct for the given vertex?
(1) line re ection
(3) dilation
(2) rotation
(4) translation
page 7
(1) no and C0 (1; 2)
(3) yes and A0 (6; 2)
(2) no and D0 (2; 4)
(4) yes and B0 ( 3; 4)
Take Home #1
20.
21.
In the diagram of ^ABC and ^DEF below,
AB = DE, OA = OD, and OB = OE.
In the diagram below, under which
transformation will ^A0 B0 C0 be the image of
^ ABC?
Which method can be used to prove
^ABC = ^ DEF?
(1) SSS
(2) SAS
(3) ASA
(4) HL
22.
page 8
(1) rotation
(3) translation
(2) dilation
(4) glide re ection
Point A is located at (4; 7). The point is
re ected in the x-axis. Its image is located at
(1) ( 4; 7)
(3) (4; 7)
(2) ( 4; 7)
(4) (7; 4)
Take Home #1
23.
In an equilateral triangle, what is the di erence
between the sum of the exterior angles and the
sum of the interior angles?
(1) 180
(2) 120
(3) 90
26.
(4) 60
24. In ^ ABC, mOA = 95, mO B = 50, and mOC
= 35. Which expression correctly relates the
lengths of the sides of this triangle?
25.
In the diagram below, ^ABC and ^XYZ are
graphed.
(1) AB < BC < CA
(3) AC < BC < AB
(2) AB < AC < BC
(4) BC < AC < AB
Use the properties of rigid motions to explain
why ^ABC = ^XYZ.
After a re ection over a line, ^A0 B0 C is the
image of ^ABC. Explain why triangle ABC is
congruent to triangle A0 B0 C0 .
page 9
Take Home #1
27.
As graphed on the set of axes below, ^A0 B0 C
is the image of ^ABC after a sequence of
transformations.
28.
Triangle ABC is graphed on the set of axes
below. Graph and label ^A0 B0 C, the image of
^ABC after a re ection over the line x = 1.
Is ^A0 B0 C0 congruent to ^ABC? Use the
properties of rigid motion to explain your
answer.
page 10
Take Home #1
29.
30.
In the diagram below, EF intersects AB and CD
at G and H, respectively, and GI is drawn such
that GH = IH.
Construct an equilateral triangle inscribed in
circle T shown below.
[Leave all construction marks.]
If mOEGB = 50 and mODIG = 115 , explain
why AB k CD.
31.
Triangle XYZ is shown below. Using a compass
and straightedge, on the line below, construct
and label ^ABC, such that ^ABC = ^ XYZ.
Based on your construction, state the theorem
that justi es why ^ABC is congruent to ^ XYZ.
page 11
Take Home #1
32.
Given: Quadrilateral ABCD is a parallelogram
with diagonals AC and BD intersecting at E
33.
In parallelogram ABCD shown below, diagonals
AC and BD intersect at E.
Prove: OACD = OCAB
Prove: ^AED = ^ CEB
Describe a single rigid motion that maps ^AED
onto ^CEB.
page 12
Take Home #1
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Take Home #1
09/29/2016
1.
Answer:
4
20.
Answer:
3
2.
Answer:
1
21.
Answer:
1
3.
Answer:
4
22.
Answer:
3
4.
Answer:
4
23.
Answer:
1
5.
Answer:
1
24.
Answer:
2
6.
Answer:
3
25.
Answer:
7.
Answer:
2
8.
Answer:
9.
Answer:
3
27.
Answer:
3
10.
Answer:
1
11.
Answer:
1
12.
Answer:
1
13.
Answer:
1
14.
Answer:
3
15.
Answer:
3
16.
Answer:
1
17.
Answer:
26.
Answer:
28.
Answer:
29.
Answer:
30.
Answer:
31.
Answer:
32.
Answer:
[answers vary] A correct explanation
is written.
18.
Answer:
2
19.
Answer:
4
33.
Answer:
[answers vary] A correct explanation
is written
[explanation]
Yes, and a correct explanation is
written
^ A0 B0 C0 is graphed and labeled
correctly.
[answers vary] A complete and
correct explanation is written
[drawing]
A correct construction of
^ ABC = ^XYZ is drawn showing all
construction arcs. A correct theorem
is stated to justify why the triangles
are congruent.
[answers vary] A complete and
correct proof is written that includes
a concluding statement, and a
correct single rigid motion is stated
[proof]