Question

grade 7 unit 1 section a checkpoint
you may use a geometry toolkit and a calculator.

1. select all the pairs of figures that are scaled copies of each other.

(note: all measurements are rounded to the nearest whole number.)

Explanation:

Step1: Check for similar angles

Scaled copies have the same set of angles. In part a, the trapezoids have angles \(60^{\circ}, 120^{\circ}\) (same set). In part b, parallelograms have angles \(60^{\circ}, 120^{\circ}\) (same set). In part c, the sets of angles \(77^{\circ}, 103^{\circ}, 47^{\circ}, 133^{\circ}\) and \(60^{\circ}, 120^{\circ}, 60^{\circ}, 120^{\circ}\) are different.

Step2: Check for proportional side - lengths

For part a:
Let the first trapezoid have sides \(a_1 = 3,b_1=12,c_1 = 9,d_1 = 9\) and the second trapezoid have sides \(a_2=7,b_2 = 9,c_2=6,d_2 = 6\). The ratios \(\frac{a_2}{a_1}=\frac{7}{3}\approx2.33\), \(\frac{b_2}{b_1}=\frac{9}{12}=\frac{3}{4} = 0.75\) are not equal.
For part b:
Let the first parallelogram have side - length \(s_1 = 10\) and the second parallelogram have side - length \(s_2=15\). The ratio of side - lengths \(\frac{s_2}{s_1}=\frac{15}{10}=\frac{3}{2}\). All sides of a parallelogram are in proportion (since opposite sides are equal in a parallelogram, and for a parallelogram, if one pair of adjacent sides is in proportion, all sides are in proportion as \(a:b=a':b'\) where \(a\) and \(b\) are adjacent sides of the first parallelogram and \(a'\) and \(b'\) are adjacent sides of the second parallelogram).

Answer:

b.