Transformations and Congruence in Geometry

The video tutorial covers geometric transformations, including translation, reflection, and rotation. It explains how these transformations preserve the shape and size of figures, making them congruent. The tutorial also demonstrates how to identify and combine transformations to achieve complex figure manipulations. Exercises are provided for practice.

Which of the following transformations preserves both the shape and size of a figure?

• Stretch

• Shear

• Dilation

• Translation

What is the line of reflection in a transformation where a triangle is reflected?

• The x-axis

• The y-axis

• The line y = x

• The line y = -x

In a rotation transformation, what is the term for the point around which the figure is rotated?

• Vertex

• Axis

• Pivot

• Center

If a figure is rotated 90 degrees clockwise, what is the direction of the rotation?

• From right to left

• From bottom to top

• From left to right

• From top to bottom

Which sequence of transformations can result in a figure being congruent to its pre-image?

• Dilation followed by rotation

• Translation followed by shear

• Rotation followed by translation

• Reflection followed by dilation

What is the result of reflecting a figure across the y-axis and then translating it 5 units to the right?

• The figure is not congruent to the original

• The figure is congruent to the original

• The figure is larger than the original

• The figure is smaller than the original

Which transformation involves changing the orientation of a figure while keeping its size the same?

• Translation

• Shear

• Dilation

• Reflection

What is the term for two figures that have the same shape and size?

• Equivalent

• Similar

• Congruent

• Identical

Which transformation does not alter the size of a figure?

• Stretch

• Shear

• Translation

• Dilation

What is the effect of a 180-degree rotation on a figure?

• The figure is enlarged

• The figure is unchanged

• The figure is mirrored

• The figure is flipped upside down