Question

is figure abcd similar to figure efgh? select the correct answer.
yes, because the figure is stretched by the same amount both vertically and horizontally.
yes, because the figure is stretched vertically but not horizontally.
no, because the figure is stretched vertically but not horizontally.
no, because the figure is stretched by the same amount both vertically and horizontally.

Explanation:

Step1: Analyze horizontal stretch

In figure \(ABCD\), the horizontal length (e.g., from \(D\) to \(C\)) is \(2 - (- 1)=3\) units. In figure \(EFGH\), the horizontal length (e.g., from \(H\) to \(G\)) is \(2-(-1) = 3\) units. So, there is no horizontal stretch.

Step2: Analyze vertical stretch

In figure \(ABCD\), the vertical length (e.g., from \(D\) to \(A\)) is \(2 - 1=1\) unit. In figure \(EFGH\), the vertical length (e.g., from \(H\) to \(E\)) is \(3 - 1 = 2\) units. So, there is a vertical stretch.

Step3: Check similarity condition

For two figures to be similar, all corresponding sides must be in proportion. Since there is a vertical stretch but no horizontal stretch, the side - length ratios are not consistent for all sides.

Answer:

No, because the figure is stretched vertically but not horizontally.