TRANSLATIONS
What is the translation rule for transforming 4 units left and 9 units up?
(x-4, y+9)
describe what happens when a point is reflected over the x-axis?
A reflection over the x-axis flips the point over the x-axis, changing the sign of the y-coordinate.
What is the new coordinates if the point (5,2) is rotated 180 degrees
(-5,-2)
What does it mean for a transformation to preserve congruence?
It means that the shape and size of the figure remain unchanged. (Rigid)
What is a transversal?
A line that crosses parallel lines.
What do you know about the interior angles of a triangle?
They sum to 180 degrees
The new point (2, 3) translated by 5 units to the right and 2 units up? What is the coordinate of the new point?
The new point would be (7, 5).
If the point (4, -3) is reflected over the y-axis, what are the coordinates of its image?
The coordinates of the image would be (-4, -3).
What word can you use to describe a rotation? [other than rotate]
Turn, Twist, Spin.
List three transformations that preserve congruence.
Translations, reflections, and rotations.
DAILY DOUBLE
When we do one or more transformations in a row to take one figure to another
Sequence of transformations.
A right triangle has one angle that is 30 degrees. What are the other 2 angles?
90 degrees and 60 degrees.
If a shape is translated 3 units left and 4 units down, what is the new position of the vertex (1, 5)?
The new position would be (-2, 1).
What happens to the coordinates (x, y) after a reflection over the y-axis?
(x, y) → (-x, y)
What important information is needed when rotating?
Center of rotation
Direction
Distance
Explain how you can determine if two shapes are congruent after a series of transformations.
By checking if all corresponding sides and angles are equal after transformations.
A point where two or more lines, edges, or curves intersect.
Vertex.
Angles that add up to 180 degrees are called ___
supplementary angles
Write the algebraic representation of a translation that moves point (x, y), right 2 units and down 4 units.
(x, y) → (x + 2, y - 4)
DAILY DOUBLE
What happens to the coordinates (x, y) after a reflection over the x-axis?
(x, y) → (x, -y)
Which rotation gives the same result as reflecting over both axes?
180 degrees
Why are translations, reflections, and rotations considered rigid transformations?
Because they maintain the original size and shape of the figure.
The figure after a transformation is called______
An image
DAILY DOUBLE
What are vertical angles, and what is true about their measurements?
They are opposite angles and they are equal.
Describe how translations affect the congruence of shapes.
Translations do preserve congruence because they do not change the size or shape of the figure.
Do reflections preserve congruence? Justify your answer.
Yes, reflections preserve congruence because they do not alter the shape or size of the figure.
How do rotations affect the congruence of shapes?
Rotations preserve congruence because they do not change the size or shape of the figure.
What transformation does not create congruent figures?
Dilation
Enlargement/Shrinking
Define Rigid Transformation
A geometric move that changes the position of a shape without changing its size or shape.
What is the definition of alternate interior angles?
two interior angles that lie on opposite sides of the transversal