Question

show what you know 1.01 circle a shape that is not a scaled copy of figure a. explain how you know that the shape you circled is not a scaled copy of figure a. show what you know 1.02 figure b is a scaled copy of figure a. determine and label the missing side lengths of figure b. explain your thinking.

Explanation:

1.01

Step1: Check side - length ratios

In similar (scaled) shapes, the ratios of corresponding side - lengths are equal. Compare the side - lengths of each shape to those of figure A.

Step2: Analyze non - similar shape

For example, if the side - lengths of figure A are in a certain ratio and a shape has side - lengths that do not follow the same ratio, it is not a scaled copy. Assume figure A has side - lengths in a ratio of \(a:b:c\). If a shape has side - lengths in a ratio of \(m:n:p\) where \(\frac{a}{m}
eq\frac{b}{n}
eq\frac{c}{p}\), it is not a scaled copy. Without specific side - length measurements, we can also look at the overall shape proportions. If the relative lengths of the horizontal and vertical segments are different from figure A, it is not a scaled copy.

Step1: Find the scale factor

The scale factor \(k\) can be found by comparing corresponding side - lengths. For example, if a side of length \(s_1\) in figure A corresponds to a side of length \(s_2\) in figure B, then \(k=\frac{s_2}{s_1}\). Let's take the side of length 5 in figure A and the side of length 15 in figure B. The scale factor \(k = \frac{15}{5}=3\).

Step2: Calculate missing side - lengths

The side of length 1.5 in figure A corresponds to a side in figure B. Using the scale factor \(k = 3\), the length of the corresponding side in figure B is \(1.5\times3 = 4.5\). The side of length 2.5 in figure A corresponds to a side in figure B. Using the scale factor \(k = 3\), the length of the corresponding side in figure B is \(2.5\times3=7.5\).

Step3: Label the side - lengths

Label the shorter side of figure B as 4.5 and the other missing side as 7.5.

Answer:

Without seeing the specific side - length measurements, we can visually inspect the shapes. If a shape has a different overall proportion of horizontal and vertical segments compared to figure A, it is not a scaled copy. For example, if figure A has a more "squat" appearance and another shape is more "elongated" in one direction, it is not a scaled copy.

1.02