Question

use the drop - down menus to explain if the two figures below are congruent, similar, or neither. if the figures are similar, state the scale factor.
answer attempt 1 out of 2
figure cdef is not congruent to figure qrst because rigid motions cannot be used to map figure cdef onto figure qrst.
figure cdef is similar to figure qrst because rigid motions and/or dilations be used to map figure cdef onto figure qrst.
the scale factor from figu figure qrst is

Explanation:

Step1: Determine similarity

Similar figures can be mapped using rigid motions (translation, rotation, reflection) and dilations. Since the problem states the figures are similar, rigid motions and dilations can be used.

Step2: Calculate scale factor

Assume coordinates: Let’s say for a corresponding side. If we consider the vertical side of \(QRST\) (e.g., \(ST\)) and \(CDEF\) (e.g., \(DE\)). Suppose \(ST = 2\) units and \(DE=1\) unit. The scale factor \(k=\frac{\text{length of side in }CDEF}{\text{length of side in }QRST}\). If we assume \(QRST\) is the original and \(CDEF\) is the image (or vice - versa, depending on mapping). Let’s assume \(QRST\) has longer sides. If \(QRST\) side length \(l_1\) and \(CDEF\) side length \(l_2\), and \(l_1 = 2l_2\), the scale factor \(k=\frac{1}{2}\)

Answer:

Figure \(CDEF\) is similar to Figure \(QRST\) because rigid motions and/or dilations can be used to map Figure \(CDEF\) onto Figure \(QRST\). The scale factor is \(\frac{1}{2}\)