Question

quadrilateral abcd is a rhombus.
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

over select one
options: translate, rotate, reflect
part b
determine which of the statements is a valid explanation or is not a valid explanation for how you know angle b maps onto angle d.
translating a copy of the figure down 3 units. select one
translating a copy of the figure 5 units to the right. select one

Explanation:

Part A

Step1: Recall rhombus properties

A rhombus has all sides equal, and its diagonals bisect the angles. To map \( BC \) to \( DC \), we consider transformations. Rotation about point \( C \) (or the center of the rhombus) can align \( BC \) with \( DC \) since \( BC = DC \) (sides of rhombus) and the angle between them can be rotated. Reflection would flip the figure, and translation would move it without rotating, so rotation is suitable.

Step2: Choose the transformation

Among Translate, Rotate, Reflect, rotating the figure (about an appropriate point, like \( C \) or the center) will map \( BC \) to \( DC \) as their lengths are equal and the angle between adjacent sides in a rhombus can be rotated to align them.

Translation moves the figure without changing its orientation or angles. Translating down 3 units will not align angle \( B \) with angle \( D \) because translation preserves the position relative to orientation, and angle \( B \) and \( D \) are not aligned by vertical translation. So this is not a valid explanation.

Translation (moving right 5 units) only shifts the figure horizontally. Angle \( B \) and angle \( D \) are not aligned by horizontal translation as their positions relative to each other involve rotational or reflective symmetry, not translation. So this is not a valid explanation.

Answer:

Rotate

Part B (First Statement: Translating a copy of the figure down 3 units)