Corresponding, Congruent, and Transformations

Which of the following best describes two figures that are congruent?

• The figures have the same shape, but different sizes.

• The figures have the same shape and size.

• The figures have different shapes but the same size.

• The figures can be perfectly overlapped after a rotation.

What is NOT a true statement about corresponding sides or corresponding angles?

• The side lengths or angles of the two figures must match each other to be corresponding.

• Corresponding sides are both from the same figure.

• Corresponding side lengths must be congruent or proportional to one another.

• Corresponding angles are always congruent to one another.

Which of the following transformations create congruent figures?

• Only translation

• Only rotation

• Translation, rotation, and reflection

• Only dilation

• Only reflection

The graph shows triangle JKL and its image after a reflection across the y-axis. What are the corresponding sides?

• JK = J'K'

• LK = J'K'

• JL = J'K'

• JK = JK

If two figures are congruent, which of the following must be true about their corresponding sides and angles?

• The lengths of corresponding sides are equal, and the measures of corresponding angles are equal.

• The lengths of corresponding sides are proportional, and the measures of corresponding angles are equal.

• The lengths of corresponding sides are equal, but the measures of corresponding angles can be different.

• The lengths of corresponding sides can be different, but the measures of corresponding angles are equal.

Which transformation does not necessarily produce a figure congruent to the original figure?

• Translation

• Rotation

• Reflection

• Dilation

Two rectangles are congruent. Rectangle 1 has a length of 8 units and a width of 3 units. What are the dimensions of Rectangle 2?

• Length = 3 units, Width = 8 units

• Length = 8 units, Width = 3 units

• Length = 6 units, Width = 4 units

• Length = 8 units, Width = 8 units

Given triangle BCD, BC is perpendicular to CD. After a reflection across the y-axis what must be true?

• Triangle BCD is congruent to triangle B'C'D'

• ∠A = ∠A'

  ∠B = ∠B'

  ∠C = ∠C'

• B'C' is perpendicular to C'D'

• All of the above

What does it mean for two polygons to be congruent?

• They have the same shape and size, and their corresponding angles and sides are equal.

• They have the same shape, regardless of size.

• They have the same size, regardless of shape.

• They can be made to overlap by cutting them into pieces and rearranging.

Which of the following is NOT a possible sequence of transformations that shows two figures are congruent?

• A rotation of 180° then a translation of 2 units right and 4 units up.

• A translation of 3 units down then a reflection across the y-axis.

• A reflection across the x-axis then a dilation k=2

• A 90° counterclockwise rotation then a translation 3 units left.