Rigid Motion and Congruence

What is rotation in rigid motion?

• Rotation is a rigid motion that turns a figure around a fixed point, called the center of rotation, by a certain angle.

• Rotation is a type of motion that involves changing the size of a figure.

• Rotation refers to the movement of a figure in a straight line without changing its orientation.

• Rotation is a motion that flips a figure over a line, creating a mirror image.

What is a rigid motion?

• A transformation that changes the shape and size of a figure.

• A transformation that preserves the distance and angles between points, meaning the shape and size of the figure remain unchanged.

• A transformation that only affects the position of a figure without altering its dimensions.

• A transformation that distorts the figure while maintaining its area.

What is the significance of the y-axis in reflections?

• Reflecting a figure over the y-axis means that each point of the figure is mapped to a point directly opposite it on the other side of the y-axis.

• The y-axis is used to measure the height of a figure in a coordinate plane.

• The y-axis represents the vertical line in a graph where all points have an x-coordinate of zero.

• Reflecting a figure over the y-axis results in a change of color for the figure.

What are the three types of rigid motions?

• Translation, rotation, and dilation

• Translation, rotation, and reflection

• Translation, reflection, and scaling

• Rotation, reflection, and shearing

What does @@r_{(x-axis)}@@ represent?

• A reflection over the y-axis.

• A reflection over the x-axis.

• A rotation around the origin.

• A translation along the x-axis.

What is a combination of rigid motions?

• A combination of rigid motions involves applying two or more rigid motions in sequence to transform a figure.

• A combination of rigid motions refers to the use of only one rigid motion at a time.

• A combination of rigid motions is the process of changing the size of a figure without altering its shape.

• A combination of rigid motions is when a figure is reflected across multiple lines simultaneously.

How can you verify that two triangles are congruent?

• By measuring the angles and sides of both triangles

• By using rigid motions such as translation, rotation, or reflection

• By comparing the area of both triangles

• By checking if the triangles have the same color

How can you determine if two quadrilaterals are congruent?

• By measuring their angles and sides to see if they are equal.

• By using rigid motions to show that one can be transformed into the other without altering its shape or size.

• By comparing their areas to see if they are the same.

• By checking if they have the same number of sides.

What is the significance of the x-axis in reflections?

• Reflecting a figure over the x-axis means that each point of the figure is mapped to a point directly opposite it on the other side of the x-axis.

• The x-axis serves as a reference line for measuring distances in the Cartesian plane.

• Reflections over the x-axis do not change the orientation of the figure.

• The x-axis is used to determine the area of shapes in geometry.

Define translation in the context of rigid motion.

• Translation is a rigid motion that rotates a figure around a point without changing its shape or orientation.

• Translation is a rigid motion that slides a figure in a straight line from one position to another without changing its shape or orientation.

• Translation is a rigid motion that reflects a figure across a line without changing its shape or orientation.

• Translation is a rigid motion that dilates a figure, changing its size but not its shape.