Question

quadrilateral abcd is a rhombus.
part a
complete the statement below using the correct dropdown options.

• to show that segment bc maps onto segment dc you would select one the entire figure

sele select one
translate
rotate
reflect
part b
determine which of the statements is a valid explanation or not a valid explanation for how you know angle b maps onto angle d .
translating a copy of the figu select one

Explanation:

Part A

Step 1: Recall rhombus properties

A rhombus has all sides equal, and its diagonals bisect the angles. To map segment \( BC \) onto segment \( DC \), we consider rotational symmetry. The center of rotation for a rhombus (about the intersection of diagonals) can rotate \( BC \) to \( DC \). Translation moves without rotation/reflection, reflection flips, but rotation (around point \( C \) or the center) is suitable. So the transformation is "Rotate".

In a rhombus, opposite angles are equal, and we can use rotation/reflection. Translating a copy doesn't map angle \( B \) to \( D \) because translation preserves orientation and position relative, but in a rhombus, angle \( B \) and \( D \) are opposite, and rotation/reflection (not translation) is needed. So "Translating a copy of the figure" is not a valid explanation.

Answer:

Rotate

Part B (Assuming a common valid/invalid case for angle mapping in rhombus)