Question

ariana uses a flag in a shadow play. the distance between the flag and the screen changes. when the distance changes, the shadow represented by figure defg forms figure defg. two figures that have the same shape, but not necessarily the same size, are called similar figures. what is the relationship between the corresponding side lengths of the figures? de is? as de. ef is? as ef.

Explanation:

Step1: Count the length of \(DE\)

Count the number of units between \(D\) and \(E\) on the grid. \(DE = 4\) units.

Step2: Count the length of \(D'E'\)

Count the number of units between \(D'\) and \(E'\) on the grid. \(D'E'= 2\) units.

Step3: Find the ratio of \(D'E'\) to \(DE\)

The ratio is \(\frac{D'E'}{DE}=\frac{2}{4}=\frac{1}{2}\), so \(D'E'\) is \(\frac{1}{2}\) (or half) of \(DE\).

Step4: Count the length of \(EF\)

Count the number of units between \(E\) and \(F\) on the grid. \(EF = 2\) units.

Step5: Count the length of \(E'F'\)

Count the number of units between \(E'\) and \(F'\) on the grid. \(E'F' = 1\) unit.

Step6: Find the ratio of \(E'F'\) to \(EF\)

The ratio is \(\frac{E'F'}{EF}=\frac{1}{2}\), so \(E'F'\) is \(\frac{1}{2}\) (or half) of \(EF\).

Answer:

\(D'E'\) is half as \(DE\). \(E'F'\) is half as \(EF\).