Transformations and Rotations in Geometry

The video covers practice problems for lesson 11, focusing on congruence and transformations in geometry. It discusses whether triangles with the same perimeter are congruent, explores rectangles with the same area but different shapes, and examines congruence through rotations and reflections. The video also explains 90-degree and 180-degree rotations, highlighting the importance of understanding coordinate changes and rigid transformations.

If two triangles have the same perimeter, are they necessarily congruent?

• Yes, they must be congruent.

• No, they can have the same perimeter but different shapes.

• Yes, because perimeter determines shape.

• No, they must also have the same area.

What transformation is applied if an image is rotated 90 degrees?

• The image is reflected.

• The image is translated.

• The image is rotated.

• The image is enlarged.

What is the result of reflecting an image over both the x-axis and y-axis?

• A dilation

• A 180-degree rotation

• A 90-degree rotation

• A translation

How do the coordinates change during a 90-degree counterclockwise rotation?

• The y coordinate becomes negative, and the x coordinate stays the same.

• The x coordinate becomes negative, and the y coordinate stays the same.

• The x and y coordinates switch places, and the new y becomes negative.

• The x and y coordinates switch places, and the new x becomes negative.

What is a rigid transformation?

• A transformation that only changes the position

• A transformation that changes the shape but not the size

• A transformation that changes the size of a shape

• A transformation that preserves both shape and size

What is the center of rotation for a 180-degree rotation?

• The origin

• The midpoint between corresponding points

• The endpoint of the shape

• The intersection of diagonals

Which of the following is true about a 180-degree rotation?

• It results in a change of size.

• It results in perpendicular sides.

• It results in a change of shape.

• It results in parallel sides.

What happens to the sides of a shape after a 180-degree rotation?

• They become shorter.

• They remain unchanged.

• They become perpendicular.

• They become parallel.

How can a 180-degree rotation be achieved using reflections?

• By reflecting over the x-axis twice

• By reflecting over the y-axis twice

• By reflecting over both the x-axis and y-axis

• By reflecting over a diagonal

What is the significance of the center of rotation in a 180-degree rotation?

• It is the midpoint of the shape.

• It is the endpoint of rotation.

• It is the starting point of rotation.

• It is where all lines intersect.