Question

Quadrilateral ABCD with parallel sides AB and

CD is shown below.
Quadrilateral RSTU is the image of quadrilateral ABCD after a transformation. Which statement is true?
B
If quadrilateral ABCD is reflected or rotated to form quadrilateral RSTU, then sides RS and TU
are not necessarily parallel.
If quadrilateral ABCD is reflected or rotated to form quadrilateral RSTU, then sides AB and RS
must be parallel or on the same line.
D
If quadrilateral ABCD is translated to form quadrilateral RSTU, then sides AB and RS are not
necessarily parallel or on the same line.
If quadrilateral ABCD is reflected, rotated, or translated to form quadrilateral RSTU, then sides
RS and T'U must be parallel.

Answer 1

• Option D

Explanation:

The rotation or reflection will change the direction of the image but the translation will leave the corresponding sides parallel.

Now the answer choices:

A

If quadrilateral ABCD is reflected or rotated to form quadrilateral RSTU, then sides RS and TU are not necessarily parallel.

• Incorrect. Since RS and TU are parallel sides of same figure, they will remain parallel regardless the mentioned transformation.

B

If quadrilateral ABCD is reflected or rotated to form quadrilateral RSTU, then sides AB and RS must be parallel or on the same line.

• Incorrect. Since AB and RS are corresponding sides of the figures, the rotation will result in different angle between those sides.

C

If quadrilateral ABCD is translated to form quadrilateral RSTU, then sides AB and RS are not necessarily parallel or on the same line.

• Incorrect. Since it is just a translation, the corresponding sides will remain parallel.

D

If quadrilateral ABCD is reflected, rotated, or translated to form quadrilateral RSTU, then sides RS and T'U must be parallel.

• Correct. Since RS and TU are parallel sides of the same figure, they must remain as is regardless the reflection, rotation or translation.