Transformations That Preserve Congruence

Tell whether the two figures are congruent.

• Yes, same size and same shape
• No, same shape but different sizes
• No, different size and different shapes

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

^{What happened from ABCD to A'B'C'D'?}

• Reflection across y axis
• Reflection across x-axis
• 180 Rotation
• Translation 2 units down

Are these shapes congruent?

• Yes
• No

Point M was reflected:

M (-5, -1) to M' (5, -1)

What type of reflection occurred?

• reflected over y-axis

• reflected over x- axis

• no reflection occurred

• 3 inches
• 5 inches
• 90 inches
• 4 inches

All corresponding angles in congruent figures are congruent.  

• True
• False

Suppose a rectangle undergoes a reflection across the x-axis and a translation 5 units down. Which of the statements is true?

• The resulting rectangle will be congruent to the original rectangle regardless of the order of the rotation and the translation.
• The resulting rectangle will be congruent to the original rectangle only if the rotation occurs before the translation.
• The resulting rectangle will be congruent to the original rectangle only if the translation occurs before the rotation.
• The resulting rectangle will not be congruent to the original rectangle regardless of the order of the rotation and the translation.

Identify a sequence of transformations that will transform figure L into figure M.

• (x, y) → (-x, y), (x, y) → (x, -y), (x, y) → (x + 3, y)
• (x, y) → (-x, y), (x, y) → (x, -y), (x, y) → (x + 1, y)
• (x, y) → (-x, y), (x, y) → (x, -y), (x, y) → (x -4 , y)
• (x, y) → (-x, y), (x, -y) → (x, -y), (x, -y) → (x + 1, y)

Select all the sequences of transformations that could take Figure P to Figure Q.

• a single reflection

• a single rotation

• a single translation

• a translation, then a reflection

• a reflection, then a different reflection