Question

are the figures similar? why or why not? (1 point) no. the rectangles are not similar because the sides are not proportional. no. the rectangles are not positioned the same. yes. the long sides are three units, and the angles are congruent. yes. the angles are congruent, and the sides are proportional.

Explanation:

Step1: Find the side lengths of the first rectangle

The vertical side length of rectangle \(ABCE\): \(A(-3,5)\), \(E(-3,2)\), so the length is \(|5 - 2|=3\). The horizontal side length: \(A(-3,5)\), \(B(-1,5)\), so the length is \(|-1-(-3)| = 2\).

Step2: Find the side lengths of the second rectangle

The vertical side length of rectangle \(FGHI\): \(F(2,2)\), \(I(2,1)\), so the length is \(|2 - 1|=1\). The horizontal side length: \(F(2,2)\), \(G(5,2)\), so the length is \(|5 - 2|=3\).

Step3: Check the proportion of side - lengths

For two rectangles to be similar, the ratios of their corresponding side - lengths should be equal. Let's check the ratios.
The ratio of the vertical side - lengths is \(\frac{3}{1}=3\), and the ratio of the horizontal side - lengths is \(\frac{2}{3}\). Since \(3
eq\frac{2}{3}\), the side - lengths are not proportional.

Answer:

No. The rectangles are not similar because the sides are not proportional.