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Geometry - 2.6-2.8 Review
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Terms in this set (34)
What is line symmetry?
when a figure can be mapped onto itself by a reflection in a line (mirror image)
What is point symmetry?
when a figure can be mapped to itself by rotating the figure
180º
* about a center point (looks the same upside down)
What is rotational symmetry?
when a figure can be mapped onto itself by rotating the figure
less than 360º
What is a line of symmetry?
lines of reflections used in line symmetry that are equidistant from all corresponding pairs of points
How many lines of symmetry are there in a rectangle?
2
How many lines of symmetry are there in a hexagon?
6
How many lines of symmetry are there in a parallelogram?
0
What is a regular polygon?
polygon in which all sides are congruent and the number of rotational symmetries is equal to the number of sides in the figure
What is the formula for finding the angles of rotation in regular polygons?
360/n
(n = number of sides in a regular polygon)
What is the minimum angle of rotation for a decagon?
36º
List the angles of rotation for a hexagon.
60º, 120, 180º, 240º, 300º, 360º
Define identity transformation.
rotation of
360º
* that maps a figure back onto itself
Does a parallelogram have point symmetry?
yes
Does a pentagon have point symmetry?
no
How many lines of symmetry does a right triangle have?
1
Given a regular pentagon, which of the following angles of rotation would
not
carry the figure onto itself?
a) 72º
b) 144º
c) 224º
d) 288º
c) 224º
What is a composition?
when a series of rigid motions takes place with one rigid motion building off one another
What is the symbol used for compositions?
◦
What is important to writing a function of a composition?
you must work
right to left!
Write this composition in function notation:
△1 → △2 : R [A, 120º]
△2 → △3 : r [BC]
△3 → △4 : T [DE]
(T [DE] ◦ r [BC] ◦ R [A, 120º])(△1)
Find the coordinates of A, the image of X (-2, 5), after the following composition of transformations: T [-2, 1] ◦ r [x-axis]
(-4, -4)
Find the image of B (2,-4) after the composition r [y = x] ◦ R [O, 90º]
B' (2, 4)
What is a glide relfection?
composition of a translation and then a reflection
What are some things to keep in mind when you are trying to determine the composition of a pre-image and an image?
- on the grid, always save translations for last! look for reflections and rotations first
- if the shape has been flipped, there was a reflection
Is the image congruent to the pre-image in compositions?
yes - all rigid motions preserve size and shape
Starting with point A (-4, -5), which single translation will produce the same image as the following sequence of translations: T <-1, 5> followed by T <4, 2> followed by T <-5, -7>?
T <-2, 0>
How can you indicate corresponding angles and sides on an image and a pre-image?
How do you write a formal congruence statement?
What is the formal definition of congruence?
two figures are congruent if there is a sequence of rigid motions that maps on to the other (rigid motions preserve size and shape)
Does the word NOON have line symmetry?
no
What is the minimum number of degrees an octagon must be rotated to carry the figure onto itself?
45º
Name the regular polygon that has a minimum rotation of 60º to carry the polygon onto itself.
hexagon
Name the regular polygon that has a minimum rotation of 120º to carry the polygon onto itself.
triangle
Remember! Positive rotations are __________ and negative rotations are __________.
Positive rotations are
counter-clockwise
and negative rotations are
clockwise
.
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