Download a) What rigid motion(s) map AF onto EF? d) What rigid motion(s

Geometry 10H
Review for Exam: Aims 12-20
1. In the figure below, all the smaller triangles are congruent to each other.
Be specific (e.g. state angle of rotation, line of reflection, vector)
a) What rigid motion(s) map AF onto EF?
A
B
b) What rigid motion(s) map FC onto CF?
c) What rigid motion(s) map ΔFBC onto ΔFDC?
C
F
D
E
d) What rigid motion(s) map ΔABF onto ΔEDF?
2. Three rigid motions are to be performed on square ABCD below. The first rigid
0
motion is the reflection through line BD. The second rigid motion is a 90 clockwise
rotation around the center of the square. Describe the third rigid motion that will
map ABCD back to its original position. Label the image of each rigid motion A, B, C, D
in the blanks.
A
B
D
C
A
B
D
C
3. Complete the table based on the series of rigid motions performed on ΔCTG
below.
Sequences of rigid C'
G'
motions (2)
Composition in function notation
C
Sequence of corresponding sides
G'' T'
C''
T''
R
T
G
Sequence of corresponding angles
Triangle congruent statement
4. For the given image:
a) How many rotational symmetries are there (include identity)?
b) How many line symmetries are there?
c) What is the minimum number of degrees that would map the figure onto
itself?
5. Using a compass and straightedge, apply TAB to triangle RLT.
R
A
L
B
T
6. Using a compass and straightedge, find the line of reflection.
7. Using a compass and straightedge, find the center of rotation.
State the measure of the angle of rotation in three ways.
Pre­image
D
R E
E
R
D
F
D
E
R
R
E
9. A rigid motion, J, of the plane takes a point, A, as input and gives C as output,
i.e. J(A) = C. Similarly, J(B) = D for input point B and output point D.
Jerry claims that knowing nothing else about J, we can be sure that AC ≅ BD
because rigid motions preserve distance.
a) Show that Jerry's claim is incorrect by giving a counterexample (hint: a
counterexample would be a specific rigid motion and four points A, B, C, and D in
the plane such that the motion takes A to C and B to D, yet AC ≅ BD).
b) There is a type of rigid motion for which Jerry's claim is always true. Which
type below is it?
(1) Rotation
(2) Reflection
(3) Translation
c) Suppose Jerry claimed that AB ≅ CD. Would this be true for any rigid motion
that satisfied the conditions described in the first paragraph? Why or why not?
D
R
E
D
F
b) Some of the illustrations are not rotations or
even a sequence of rigid transformations. Pick one
such illustration and use it to explain why it is not
a sequence of rigid transformations.
F
E
F
F
R
a) Which illustrations show a single rotation?
D
F
8. Each of the illustrations show in black a
plane figure consisting of the letters F, R, E, and D
evenly spaced and arranged in a row. In each
illustration, an alteration of the black figure is
shown in gray.
10. Using a compass and straightedge, perform the following composition of rigid
o
motions: rl (RP,60 (Tv (ΔABC)))
B
v
A
C
P
l
11. For the pair of figures below, name the center of rotation and find the angle of
rotation using a straightedge and protractor. Name it three ways.
C'
A
A'
B
C
12. Using a compass and straightedge, apply TAB to circle C.
13. Draw the vectors that define each translation:
14. Next to each figure, write if it has line and/or rotational symmetry. List all
angles of rotation, including the identity.
15. Given the figure below, line l is the perpendicular bisector of AB and CD. Prove
AC = BD using rigid motions.
16. Construct a line through point P below that is parallel to the line m three ways:
0
a) rotating line m by 180
P
m
b) By creating equal corresponding
angles:
P
m
c) By creating 2 perpendicular lines:
P
m
17. Using a compass and straightedge, reflect triangle B across line l.
l
18. Complete: Two lines are perpendicular if they _______________ and any of
0
the angles formed is a __________ or ___ angle. A perpendicular bisector
also functions as a line of _____________ with each pre-image point the same
distance from the line as its image on the opposite side of the line.
• Construct the perpendicular bisector of segment AB:
A
B
• The two points, A and B are ___________________ from the
_______________________ or ____________________________.