Answer:
Therefore, none of the figures are similar.
Explanation:
To determine if two figures are similar, we need to check if their corresponding sides are proportional and their corresponding angles are congruent. If both of these conditions are true, then the two figures are similar.
First, let's plot the three rectangles on the coordinate plane:
A | B
(-4,4) | (0,4)
--------|-------
(-4,2) | (0,2)
--------|-------
(-2,1) | (0,1)
C |
(-6,6) | (0,6)
--------|-------
(-6,3) | (0,3)
|
Now, let's compare the sides of the rectangles:
Rectangle A has side lengths of 4 units and 2 units.
Rectangle B has side lengths of 2 units and 1 unit.
Rectangle C has side lengths of 6 units and 3 units.
Since none of the rectangles have the same side lengths, we can immediately see that none of the rectangles are congruent with each other. However, we can still determine if any of the rectangles are similar.
To check for similarity, we need to compare the ratios of corresponding side lengths. For example, the ratio of the length of the top side of rectangle A to the length of the top side of rectangle B is:
4 / 2 = 2
The ratio of the length of the left side of rectangle A to the length of the left side of rectangle C is:
4 / 6 = 2/3
If we calculate the ratios of all corresponding side lengths, we get:
Rectangle A to rectangle B: 2
Rectangle A to rectangle C: 2/3
Rectangle B to rectangle C: 1/3
Since none of these ratios are equal to each other, we can conclude that none of the rectangles are similar to each other.