Proving Congruency in Transformations

After a series of rigid transformations, ΔDOG is mapped onto ΔD'O'G'.

Find x.

• 2.5

• 6

• 4

• 6.5

Which translation maps ΔABC onto ΔDEF?

• (x, y) → (x - 6, y + 5)

• (x, y) → (x + 6, y - 5)

• (x, y) → (x + 4, y - 3)

• (x, y) → (x - 4, y + 3)

What is the value of x?

• 24

• 38

• 57

• 114

Determine if the two figures are congruent by using transformation. If so, what kind of transformation?

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

• congruent; reflection

• congruent; translation

• not congruent

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

• congruent; a rotation

• congruent; a reflection followed by translation

• not congruent

• congruent; a reflection

Which statement about figure 1 and 2 must be true?

• A series of transformations will transform 1 to 2, and the figures will be congruent.

• A 180º clockwise rotation will transform 1 to 2, and the figures will be congruent.

• A series of transformations will transform 1 to 2, but the figures will not be congruent.

• A 90º clockwise rotation will transform 1 to 2,

  but the figures will not be congruent.

Are the figures congruent? (What type of transformation is shown?)

• NOT Congruent (dilation)

• NOT Congruent (translation)

• Congruent (dilation)

• Congruent (translation)

• A

• B

• C

• D

Which set of transformations could be applied to figure A to map it onto A'?

• reflect over y-axis, then translate down 2 units

• reflect over y-axis, then translate down 6 units

• rotate 180º about the origin, then reflect over x-axis

• rotate 90º CW about the origin, then relfect over x-axisfl