Question

spiral review

1. here is an unlabeled rectangle and several quadrilaterals that are labeled

in the table, mark the quadrilaterals that are scaled copies of the unlabeled rectangle. then, for all scaled copies, write the scale factor used to create it.
is it a scaled copy?
scale factor

Explanation:

Step1: Determine scaled - copies

Check the shape and side - length ratios of each quadrilateral compared to the unlabeled rectangle. A scaled copy has the same shape (same angle measures) and side - lengths in proportion.

Step2: Calculate scale factors

For a scaled copy, find the ratio of corresponding side - lengths between the scaled copy and the unlabeled rectangle. Let's assume the unlabeled rectangle has length $l_0$ and width $w_0$, and a scaled copy has length $l_1$ and width $w_1$. The scale factor $k=\frac{l_1}{l_0}=\frac{w_1}{w_0}$ (assuming uniform scaling).

Let's assume the unlabeled rectangle has length 4 units and width 2 units.

• Quadrilateral A: Not a rectangle (it's a parallelogram), so not a scaled copy.
• Quadrilateral B: Length is 8 units and width is 4 units. Scale factor $k = 2$ since $\frac{8}{4}=\frac{4}{2}=2$. It is a scaled copy.
• Quadrilateral C: Length is 6 units and width is 3 units. Scale factor $k = 1.5$ since $\frac{6}{4}=\frac{3}{2}=1.5$. It is a scaled copy.
• Quadrilateral D: Length is 2 units and width is 1 unit. Scale factor $k = 0.5$ since $\frac{2}{4}=\frac{1}{2}=0.5$. It is a scaled copy.
• Quadrilateral E: Length is 4 units and width is 2 units. Scale factor $k = 1$ since $\frac{4}{4}=\frac{2}{2}=1$. It is a scaled copy.
• Quadrilateral F: Not a rectangle (it's a trapezoid), so not a scaled copy.
• Quadrilateral G: Length is 4 units and width is 2 units. Scale factor $k = 1$ since $\frac{4}{4}=\frac{2}{2}=1$. It is a scaled copy.
• Quadrilateral H: Length is 8 units and width is 4 units. Scale factor $k = 2$ since $\frac{8}{4}=\frac{4}{2}=2$. It is a scaled copy.

	A	B	C	D	E	F	G	H
Scale Factor	-	2	1.5	0.5	1	-	1	2

Answer:

	A	B	C	D	E	F	G	H
Scale Factor	-	2	1.5	0.5	1	-	1	2