Rigid Transformations
Rotations
Reflections
Congruence
Describing a Rigid Transformation
100
State the 3 rigid transformations discussed in class.
Translation
Reflection
Rotation
100
What is the rule for Rotations?
a) 90 degrees clockwise
b) 90 degrees counterclockwise
c) 180 degrees clockwise/counterclockwise
*all around the origin
a) 90 degrees clockwise
(x,y) ---> (y,-x)
b) 90 degrees counterclockwise
(x,y) ---> (-y,x)
c) 180 degrees clockwise/counterclockwise
(x,y) ---> (-x,-y)
100
What are the rules for reflections?
a) x-axis
b) y-axis
a) x-axis
(x,y) ---> (x,-y)
b) y-axis
(x,y) ---> (-x,y)
100
What is the definition of congruent?
Congruent:
-same size and shape
-corresponding sides and angles have the same measure
100
What are the 2 components needed when describing a rigid transformation?
a) State the rigid transformation
b) State the details
Ex:
a) Translation
b) 5 units to the right
200
Draw an example of:
a) translation
b)reflection
c)rotation
answers will vary
200
Point (-6, 7) is rotated 180° about the origin in a counterclockwise direction. What are the coordinates of its image?
(6,-7)
200
What are the coordinates of A', the image of A(12, 7) after a reflection in the x-axis?
A' (12,-7)
200
Draw an example of 2 figures that are congruent.
Answers will vary
200
Which expression best describes the transformation shown in the diagram below?
Reflection across the x-axis
300
What are the "movements" of the rigid transformations?
a) Translation -
b) Reflection -
c) Rotation -
a) Translation - SLIDE
b) Reflection - FLIP
c) Rotation - TURN
300
Leah rotates △ABC 180 degrees counterclockwise around the origin to form △A'B'C'.
A (2,3) , B (5,8), C (9,2)
What are the coordinates of the vertices of △A'B'C'?
A' ( , ), B' ( , ), C' ( , )
A' ( -2 , -3 )
B' ( -5 , -8 )
C' ( -9 , -2 )
300
What are the coordinates of A' and B', the image of A(-1, -5) and B (-4,-9) after a reflection in the y-axis?
A' (1,-5)
B' (4, -9)
300
If ΔGHI 
ΔJKL, then ∠L is congruent to which angle?
∠I
300
Describe the rigid transformation that occurred.
Translation 7 units to the right
400
Which is a 180° rotation of the figure 
?
C.
400
Blake rotates △ABC 90 degrees counterclockwise around the origin to form △A'B'C'.
A (-4,6) , B (-8,8), C (-3,1)
What are the coordinates of the vertices of △A'B'C'?
A' ( , ), B' ( , ), C' ( , )
A' ( -6 , -4 )
B' ( -8 , -8 )
C' ( -1 , -3 )
400
Bob reflects △ABC across the x-axis to form △A'B'C'.
A (1, 2) , B (5,9), C (2,4)
What are the coordinates of the vertices of △A'B'C'?
A' ( , ), B' ( , ), C' ( , )
A' ( 1 , -2 )
B' ( 5 , -9 )
C' ( 2 , -4 )
400
1) Are the following rectangles congruent?
2) Explain why.
The rectangles are NOT congruent.
The rectangles are not the same size and one pair of corresponding side lengths are not the same measure.
400
Which type of transformation is illustrated in the accompanying diagram?
Rotation 90 degrees clockwise around the origin
500
In the diagram, which triangle is the image of Δ2 after a reflection in the x-axis?
Triangle 3
500
Emma rotates △ABC 90 degrees clockwise around the origin to form △A'B'C'.
A (-3,-6) , B (-1,-4), C (-5,-7)
What are the coordinates of the vertices of △A'B'C'?
A' ( , ), B' ( , ), C' ( , )
A' ( -6 , 3 )
B' ( -4 , 1 )
C' ( -7 , 5 )
500
Kayla reflects △ABC across the y-axis to form △A'B'C'.
A (5, 2) , B (8,1), C (4,7)
What are the coordinates of the vertices of △A'B'C'?
A' ( , ), B' ( , ), C' ( , )
A' ( -5 , 2)
B' ( -8 , 1 )
C' ( -4 , 7 )
500
The angle measurements of triangle ABC are shown below:
If triangle DEF is congruent to triangle ABC, what is the measure of angle E?
90°
500
Which type of transformation is illustrated in the accompanying diagram?
Rotation 90 degrees counterclockwise around the origin