Reflections
This type of transformation flips a figure over a line, creating a mirror image.
What is a reflection?
This transformation moves every point of a figure the same distance in the same direction.
This transformation moves every point of a figure the same distance in the same direction.
This transformation turns a figure around a fixed point, changing its orientation but keeping its size and shape.
What is a rotation?
These transformations, including reflections, rotations, and translations, preserve the size and shape of a figure, making it congruent to its original.
What are rigid motions?
These theorems are used to prove that two triangles are identical in size and shape, which means they are this.
What is congruent?
This is the line over which a figure is reflected.
What is the line of reflection?
In a translation, this term describes the movement of a figure along a specific path, without any rotation or reflection.
What is a slide?
The fixed point around which a figure rotates is called the center of this transformation.
What is the center of rotation?
Two figures are congruent if one can be mapped onto the other by a combination of these three types of rigid motions.
What are translations, rotations, and reflections?
This theorem states that two triangles are congruent if two angles and the included side are congruent.
What is the Angle-Side-Angle (ASA) Congruence Theorem?
Reflecting a point across the y-axis changes the sign of this coordinate.
What is the x-coordinate?
When translating a point by (3, -2), this means the x-coordinate increases by 3, and the y-coordinate decreases by 2.
What is a translation of 3 units right and 2 units down?
When a point is rotated 90 degrees counterclockwise around the origin, the new coordinates are found by swapping the x- and y-coordinates and changing the sign of the new x-coordinate.
What is the rotation rule (x, y) → (-y, x)?
This property of rigid motions ensures that the size and shape of a figure remain unchanged during transformations.
What is congruence?
This theorem is used to prove congruence if three sides of one triangle are congruent to three sides of another triangle.
What is the Side-Side-Side (SSS) Congruence Theorem?
When reflecting a point across the x-axis, this coordinate changes sign.
What is the y-coordinate?
The direction and distance of a translation are described by this mathematical concept, which is often written in the form (x, y).
What is a translation vector?
A rotation of 180 degrees around the origin results in this transformation of a point's coordinates.
What is (x, y) → (-x, -y)?
When a figure undergoes a rigid motion, it maps onto an image that is exactly the same in size and shape, meaning the two figures are this.
What are congruent figures?
This theorem can be used to prove congruence when two sides and the angle between them are congruent in two triangles.
What is the Side-Angle-Side (SAS) Congruence Theorem?
This type of reflection occurs when a figure is reflected across a vertical line, such as the y-axis.
What is a reflection across a vertical line?
The translation rule that moves a point 5 units to the right and 3 units up can be written as this coordinate transformation.
What is (x + 5, y + 3)?
A 270-degree clockwise rotation around the origin is equivalent to this counterclockwise angle.
What is a 90-degree counterclockwise rotation?
These parts of congruent figures, such as sides and angles, remain equal in measure after a rigid motion transformation.
What are corresponding parts?
This criterion does not prove triangle congruence because having the same angles doesn't guarantee that the triangles are the same size, only that they are similar.
What is the Angle-Angle-Angle (AAA) criterion?