Congruency and Similarity Transformations

Quad OBCD is similar to Quad OHTE because:

• Quad OBCD can be reflected over the x axis and then rotated 90 degrees

• Quad OBCD can be reflected over the x-axis and then dilated about point O by a scale factor of 2.

• Quad OBCD can be reflected over the y-axis and then dilated about point O by a scale factor of 2.

• Quad OBCD can be reflected over the y-axis and then dilated about point O by a scale factor of 1/2.

Circle M is dilated by a scale factor of 3/2 and then translated along the vector <-1,3> to form circle M'. Which of the following is true?

• Circle M and circle M' are similar.

• Circle M and circle M' are congruent.

• Circle M and circle M' are concurrent.

• None of the above

Choose the correct similarity transformation.

• Dilation using scale factor of 5/2 followed by a rotation 90 CCW

• Dilation with a scale factor of 5/2 followed by a y-axis reflection

• Dilation with scales factor of 5/2 followed by 90 CCW rotation and then a translation 3 units to the left and 3 units down

• 90 CCW rotation  followed by 5/2 dilation

Does the rule (x, y) --> (5x, 5y) produce a similar, congruent, or neither image

• Similar with a SF of 5

• Congruent

• Neither

Which of the following is one possible sequence of transformations?

• Dilation with scale factor 2, then Reflection over the y-axis

• Dilation with scale factor 2, then Reflection over the x-axis

• Dilation with scale factor 1/2, then Reflection over the y-axis

• Dilation with scale factor 1/2, then Reflection over the x-axis

Which is a not a true statement about the figures shown below?

• The image is smaller than the pre-image.

• Triangle GHI is similar to Triangle G’H’I’.

• The transformation shown is a dilation.

• Segment GH is congruent to segment G’H’.

Mrs. Johns was able to map circle P onto circle R (with Q and s being on each circle, respectively) using a translation and a dilation. Mrs. Johns concluded: "I was able to map circle P onto circle R using a sequence of transformations and a dilation, so the figures are similar." What error did Mrs. Johns make in her conclusion?

• Mrs. Johns used translations so the circles aren't similar.

• Mrs. Johns used dilations so the circles aren't similar.

• There is no error. This is a correct conclusion.

Determine if the two figures are congruent by using transformations. Explain your reasoning

• congruent; a rotation

• not congruent

• congruent; a reflection followed by translation

• congruent; a reflection

Determine if the two figures are congruent by using transformations. If so, explain the transformation or transformations that map the first figure onto the second figure.

• congruent; a counterclockwise rotation of 90° followed by a translation

• congruent; reflection

• congruent; translation

• not congruent

If you rotate this figure counterclockwise as shown, will it produce a congruent figure?

• yes

• no