We are given the vertices of three rectangles.
& Rectangle A: (0,0), (4,0) , (4,2), (0,2)
& Rectangle B: (0,0), (- 6,0), (- 4,3), (0,3)
& Rectangle C: (0,0), (4,0), (4,2), (0,2)
Let's plot the given points in a coordinate plane and connect them with segments to draw each rectangle.
We want to determine which of the given figures are similar. Remember that two figures are similar if the corresponding sides are proportional.
l_1/l_2= w_1/w_2
Here, l represents the length of the rectangle and w is the width. Since all the given rectangles have the origin as a vertex, the length will be the distance from the origin to the vertex with the form (x,0) and the width will be the distance from the vertex with the form (0,y).
We can analyze the condition of proportionality for each pair of rectangles to see if they are similar. Let's start with Rectangles A and B. In this case, we will substitute l_1= 6, l_2= 4, w_1= 3, and w_2= 2 into the equation to see if the condition is met.
Since the sides are proportional, Rectangle A and Rectangle B are similar! Now we will do the same for Rectangle B and Rectangle C. Let's substitute l_1= 6, l_2= 4, w_1= 3, and w_2= 2 into the proportion equation.
This proportion equation is also true, which means that Rectangles B and C are also similar. Finally, notice that Rectangles A and B are the same rectangle. This means that the corresponding sides are equal, so they are similar. Therefore, the three rectangles are all similar!
