Rigid Transformations and Congruence

​Vocabulary

• Transformation - an operation that maps an original figure onto a new figure ​

• Original Figure - is called the PRE-IMAGE

• New Figure - is called the IMAGE​

• Rigid Transformation - a transformation that creates an image that is congruent to the pre-image. (translation, reflection, and rotation ONLY)​

THESE ARE THE ONLY 3 TRANSFORMATIONS THAT CREATE CONGRUENT IMAGES! RIGID TRANSFORMATIONS

​Types of Transformations

​Translation - a slide that moves all points in the same direction and same distance

​Reflection - a FLIP over a certain line, all points from the pre-image to image are the same distance apart.

​Rotation - a TURN around a fixed point, all points from the pre-image to image are the same distance apart.

Multiple Choice

How many degrees was the figure rotated?

• 90 degrees counterclockwise 
• 180 degrees
• 90 degrees clockwise

Multiple Choice

What is this picture an example of? 

• An angle
• A cat vertex 
• Rotation 
• Dilation

Multiple Choice

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

• Translated 5 units down and 5 units to the right
• Translated 5 units down and 1 to the right
• Translated 8 units down and 5 units to the right
• Translated 5 units down and 4 units to the right

Multiple Choice

Which answer shows a reflection across the x-axis?

• d
• c
• b
• a

Multiple Choice

Shapes that are the same shape and the same size are ________.

• similar
• unique
• congruent
• corresponding

Multiple Choice

Determine how to translate triangle ABC to triangle A'B'C'.

• left 2, up 9
• right 2, down 9
• left 2, down 9
• left 2, up 5

Multiple Choice

A flip is also called a __________.

• rotation

• translation

• dilation

• reflection

Multiple Choice

If you rotate a shape 360^o, it will look like nothing happened to the shape.

• True

• False

Multiple Select

Choose all of the transformations that are rigid, meaning they keep the shape congruent.

• Scaling up or down

• Translation

• Rotation

• Reflection

Multiple Choice

When talking about figures on a coordinate plane, what does "congruent" mean?

• Same shape, same size
• Same shape, size changes
• Different shape, different size
• Same shape, different size

Multiple Choice

The side length of a square is 5 units. If the square rotates 90 degrees clockwise, what will be the length of that corresponding side in the new square?

• 1 unit

• 5 units

• 10 units

• 20 units

Multiple Choice

An equilateral triangle has 3 equal sides and 3 equal angles. If an equilateral triangle was reflected over the y-axis, what will be the measure of each angle of the image?

• 60 degrees
• 90 degrees
• 120 degrees
• 180 degrees

Multiple Choice

What is the rule for the following reflection?

• Reflection across the x-axis

• Reflection across the y-axis

Multiple Choice

What will be the new position of the given point after a reflection across the y-axis?

Multiple Choice

Which series of transformations were performed in the figure?

• Translation 5 units down, reflection over the y-axis

• Reflection over the x-axis, translation 6 units right

• Rotation 90^o clockwise, reflection over the x-axis

• Rotation 180^o clockwise, reflection over the y-axis

Multiple Choice

A turn is also called a ___________.

• Translation
• Reflection
• Rotation
• Transformation

Multiple Choice

A slide is also called a _________.

• Translation
• Reflection
• Rotation
• Transformation

Multiple Choice

Which of the following images shows a rotation of 180^o?

Multiple Choice

Imagine the shape above is rotated 90^o counterclockwise. How do the side lengths of the original shape compare to the side lengths in the new shape?

• Some of the side lengths increase in measure and other side lengths decrease in measure.

• The measures of the side lengths double.

• The measures of the side lengths decrease by one third.

• The measures of the side lengths are the same.

Multiple Choice

A 115 degree angle is translated 4 units right and 1 unit down. What is the measure of the angle after the translation?

• 41 degrees

• 14 degrees

• 15 degrees

• 115 degrees

Multiple Choice

Describe the transformation in the image.

• Translation

• Reflection

• Rotation

Multiple Choice

• Figures 1 and 4
• Figures 2 and 5
• Figures 2 and 3
• Figures 3 and 5

Multiple Choice

What transformation is happening to the red triangle to get to the blue triangle?

• Translation
• Rotation
• Reflection

Multiple Choice

 Describe the Transformation

• Translation
• Rotation
• Reflection

Multiple Choice

 Describe the Transformation

• Translation
• Rotation
• Reflection

Multiple Choice

Rotation or Reflection

• Rotation
• Reflection
• translation

Multiple Select

Diego made the shape on the left, and Elena made the shape on the right. Each shape uses 5 circles. Select all the true statements.

• Elena’s design is a translation of Diego's design.

• Diego’s design is congruent to Elena’s design.

• The smallest circle in Diego's design is congruent to the smallest circle in Elena’s design.

Multiple Choice

Which of the following is a way to show that Polygon A is congruent to Polygon B.

• Just by looking at it.

• By using a rigid transformation.

• By counting up all the sides.

• They are not congruent.

Multiple Choice

Decide whether or not Shape A is congruent to Shape B.

• Yes, they are congruent.

• No, they are not congruent.

Multiple Choice

Decide whether or not Shape A is congruent to Shape B.

• Yes, they are congruent.

• No, they are not congruent

Multiple Select

Which of the following is a great strategy for determining if shapes are congruent. Select all strategies that will work.

• Just look at it you can always tell right away.

• Measuring angles and sides to make sure they match.

• Using tracing paper and a sequence of rigid transformations

• By guessing.

Multiple Choice

• The smallest circle in Diego's design is congruent to the smallest circle in Elenna's design

• Diego's design is congruent to Elena's design

• Elena's design is a translation of Diego's design