3.1
what is a rigid motion?
A rigid motion is the movement of a shape that keeps the side lengths and angle measured the same
How do you notate a translation?
T<x,y>
What is the center of rotation?
A centroid
What is a Glide Reflection
Any translation that keeps the shape the same size
Define Point Symmetry
The figure is able to be mapped onto itself by rotating the figure 180 degrees about a center point.
What is the name of the shape before any rigid motions?
Preimage
What is the rule for the following translation: A(18,2) B(5,7) C(5,7) Aβ(12,4) Bβ(1,9) Cβ(1,8)
T<-6,2>
If a triangle is rotated 180 degrees about its centroid, what is the relationship between the original and final positions of the triangle's vertices?
The triangle will be in its original position.
What is Theorem 3-3
The composition of two or more rigid motions is a rigid motion
What angles of rotation does an equilateral triangle have
120 degrees and 240 degrees.
what is the general rule for when reflecting across the x-axis?
(x,y)---->(x,-y)
How do you notate multiple translations?
(T<x,y> Λ T<x,y>)
A square is rotated 45 degrees counterclockwise about its center. What is the angle between the original and final positions of two adjacent sides?
The angle between the original and final positions of two adjacent sides is 45 degrees.
What is Theorem 3-4
Any rigid motion is either a translation, reflection, rotation, or glide reflection
What type of symmetry does this figure have (if any)
If so, how many lines of symmetry does it have?
Figure: T
Line Symmetry, 1 line on symmetry
what are the vertices of Rectangle G(2, -1), H(7, -1),
I(7, -4), and J(2, -4) reflected across the line y = x.
Gβ(-1,2), Hβ(-1,7), Iβ(7,-4), Jβ(-4,2)
What is one possible set of two translations that turn A(2,5) B(6,-6) C(-4,12) into Aββ(9,-3) Bββ(13,-14) Cββ(3,4)
multiple answers
Consider a regular hexagon. If it is rotated 60 degrees counterclockwise about its center, what is the angle of rotation between any two consecutive sides?
The angle of rotation between any two consecutive sides of the hexagon is 60 degrees.
Graph the following points of triangle ABC: A(-1,5), B(-8,7), C(-5,2). Then perform the following glide reflection: Translate 6 units down and reflect across the y-axis
Aβ(2,0), Bβ(8,1), Cβ(5,-4)
A flower has 9 congruent petals. How many Lines of symmetry does it have? What are it's degrees of rotation?
Rotational
9 Lines of symmetry
40, 80, 120, 160, 200, 240, 280, and 320 degrees
What are the coordinates of BβCβDβ when B(-4,2), C(4,7), D(5,1) when it is reflected across the x-axis
Bβ(-4,-2), Cβ(4,-7), Dβ(5, -1)
Put the numerical values (no variables) to Aββ Bββ and Cββ if you had repeated the translation below to Aβ Bβ and Cβ
A(3,Q) B(R,Q) C(Q,3) Aβ(P,R-2) Bβ(R,P) Cβ(Q,5)
Aββ(3,5) Bββ(5,5) Cββ(1,7)
For an irregular polygon with seven sides, perform a counterclockwise rotation about its centroid by an angle that aligns one of its sides with its mirror image. What is the measure of this rotation angle?
The measure of the counterclockwise rotation angle needed to align one side of the irregular polygon with its mirror image is 180/7 degrees.
Graph the following preimage of triangle ABC: A(-2,3), B(0,7), C(3,5) and the image Aβ(-6,-1), Bβ(-8,-6), Cβ(-11,-4)
Reflections across x=1 and y=-4
A Star has 60 points. How many lines of symmetry does it have? What are its degrees of rotation?
60 Lines of symmetry
12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, and 354 degrees.