Name:
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Period:_ _ _ __
Exam 4 - STUDY GUIDE
Geometry: Modeling Geometric Figures and Applying Transformations
L The distance between two cities is 450 miles. On a
are 9 inches apart. What is the scale of the map?
450/q
2. Draw the shape made by
3. What are the actual dimensions ofthe study area?
FLOOR PLAN OF LIBRARY
3cm--t
Check~()ut
Are,a
Scale: 1 em : 5 III
4. Draw the shape made by slicing a triangular prism parallel to its bases.
~
5.
congruent?
original to the image, and tells whether the two figures are similar or
6. Which describes the transfonnation from the original to the image, and tells whether the two figures are similar or
congruent?
7. The translation (x - 20, Y+ 13) is applied to a triangle. Maryanne
image of the triangle, tests the conjecture, and finds that it is true. What
"I:
8. Which ofthe following is the correct description of the graph shown?
\' a. Figure A'B' C'D' is the image of figure ABCD
under a rotation of 90° clockwise about the
origin.
b. Figure A'B'C'D' is the image of figure ABCD
under a rotation of 90° counterclockwise about
the origin.
c. Figure A'B'C'D' is the image offigureABCD
under a rotation of 45° counterclockwise about
~heorigin.
~igure A'B'C'D' is the image of figure ABCD
under a rotation of 180° about
9. A figure is composed of a square and a line that goes through the left side of the square.
The figure is reflected across the
Which describes the line in the image?
( n-t ~e-, Jt,vD '" IS
xWC~O
~ U¥fTS -a Af;../A-1-(
F/loM.. ~ 0i2t ~(/ik IMA-t!id-,
f....,uv G 0 F
10. Write a congruence statement for the pair of congruent polygons.
II. 6ABC == !1DEF. What is the value f x?
3)<. =
o
A
~ ~
x.--1­
21
.-~~,.,-~.
B
30
c
E
4x
2
2.J
F
~x
- G:, "":. 3~
~x.=-4-2)(,,:1-
4k+Q....
~'3V
4x-:::2-g'
X--= .~
12. IdentifY the transformation from the original to the image, and tell whether the two figures are similar or
congruent. The original figure has solid sides; the image has dashed sides.
y
13. A square has vertices T(I, 2), U(4, 2), V(4, 5), W(I, 5). If the square is rotated clockwise 90 degrees around (0,0),
what are the coordinates of W?
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14. Triangle EFG has vertices E(-3, 1
reflection across the
15. Suppose a constellation of stars is plotted on a coordinate plane. The coordinates
representing the star is then translated right 5 units. What are its new <'(",,-rli,"<.>"",
-7). The point
16. A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located
at (3,4)?
!
\
l7. Which set of points represents a reflection of the triangle in the x-axis?
18. Draw the image of a triangle with vertices (2, 3), (3,5), and (5,3). Then perform the following transformation: a
180 0 clockwise rotation about the origin.
19. In the figure, the angles are formed by a transversal and two parallel lines. Which angles seem to be
20. rfline m II line n ~L2 measures 4?=', what is the measure of L5?
21. Ifline m II line
PI
and L2 measures 35°, what is the measure of L5?
tJ/S""'
1
m~----------------~~4~~------~
I'¥$'"'
22. Which of the angles in the figure are supplementary to L3?
m~--------------~~~~~-------.
23. Which of the angles in the figure are supplementary to L7?
24. Ifx = 40, what is the value ofy?
25. The height of a tower on a scale drawing is 10 centimeters. The scale is 2 cm: 13 m. What is the a<.iual height of the
tower?
Z
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~- /3 r
~
0;:.
X .-
X -:: : :
.e:=)
-
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26. Drew designs a rectangular vegetable garden with a width of3 inches and a length of2.5 inches. The design and
the full-size vegetable garden are similar. If the width of the full-size vegetable garden is 54 feet, what is its length
to the nearest foot?
Vegetable Garden Design
'N
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=81".. c~ S
!)
L ': 2 .. £5 ,,,,'cl,.......s
3
3 in. ~
_ 2.5"
-~
?4
-
'5 Yf...f
xtt
x.. ~
c
(
"'$
)C ~
2. )
"A.
l<6 C0 ~')
27. Use a protractor to draw a 85° angle.
28. Draw a 90° clockwise rotation about the point shown.
29. Draw a translation of the figure.
30. Sketch the trapezoid in the coordinate plane after it is reflected about the y-axis.
31. Graph triangle PQR with
p( -:5,
translation, 12 units to the right and 10 units
rl"",i'Tr" :··t:;.~·/~.
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32. In triangle ABC, the measure of LA is 20° greater than the measure of LB. The measure of LC is twice the
measure of LB. Find the meas~r~~f~~~h.an~I~. ~ f 800 =::':;:;~m_:;:J
. •.:.A.•.. f.•.~.4Li:::,.~N~;~~~'i\,~··· (8+2.0)+ B --t- (f!.B) '::: [-gO" 4e ~ 2-0 -=-l'BO o_ _~ 4e;;- w
(J
33. What happens to a figure that is reflected across the y-axis twice? Explain why this occurs.
34. Leroy graphed a square with an area of 64 square units. He then applied transformations to graph an image square
~:i;:",ea of 8 ~:~e;nits CO~d :~ ::red traosi"'ions, retlections, aod <otations to gctthis image?
f
dilatio~affect
35. How does a
the perimeter~nd area of the image it produces? Use a coordinate grid to show a
rectangle under a dilation to justify your answer.
36. l!'lL::A = 71° and l!'lL::B = 38°. Find l!'lL::BCR.
B
Iv,/' 1'ic~
P = (0<:.­
'-I e _
( /~/ \ ... rp = 34.g
A
c
R
11+3'3&'/O~
1go'"
10'1
~
"",LBcA
= 11 u
So
L(';:,CA ~ LBc~ ~
c"'­