TRANSLATIONS
What is a translation in Geometry?
A translation is a transformation that slides every point of a shape the same distance
What is a reflection over the x-axis?
A reflection over the x-axis flips the shape over the x-axis, changing the sign of the y-coordinate.
What is a rotation of 90° counterclockwise in the coordinate plane?
What does it mean for a transformation to preserve congruence?
It means that the shape and size of the figure remain unchanged. (Same size, same shape)
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?
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).
If the point (1, 2) is rotated 180° around the origin, where is the new position?
The new position would be (-1, -2).
List three transformations that preserve congruence.
Translations, reflections, and rotations.
A rigid motion
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 is the algebraic rule for a reflection over the y-axis?
(x, y) → (-x, y)
Explain how you would rotate the point (-3, 4) 270° clockwise and state the new point.
You turn your paper to the right 3 times, the image is at (-4, -3).
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.
What is a transformation?
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 is the algebraic rule for a reflection over the x-axis?
(x, y) → (x, -y)
What word can you use to describe a rotation? [other than rotate]
Turn
Spin
Why are translations, reflections, and rotations considered rigid motions?
Because they maintain the original size and shape of the figure.
The figure after a transformation is called______
An image
What are vertical angles and what is true about their measurements?
They are across from each other. 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
What is a tessellation?
A repeating pattern of one or more shapes that goes on forever in all directions.
DAILY DOUBLE!!!
What is the definition of alternate interior angles?
Angles formed by parallel lines that are cut by a transversal. They are between the parallel lines on the opposite sides of the transversal. They are equal.