Determine whether the pair of figures is similar or not. Explain your reasoning.
Rectangle DEFG is shown with side DE labeled 15, side EF labeled 8, side FG labeled 15, and side GD labeled 8. Rectangle WXYZ is shown with side WX labeled 7.5, side XY labeled 4, side YZ labeled 7.5, and side ZW labeled 4.
1. No, the shapes are not similar because they are different sizes.
2. Yes, they are similar because they are both rectangles.
3. Yes, they are similar because they have proportional side lengths and equal angle measures.
4. No, they are not similar because we don’t know the measures of their angles.
The correct answer is 3. Yes, they are similar because they have proportional side lengths and equal angle measures.
To determine if two figures are similar, we need to compare their side lengths and angles. In this case, we can see that Rectangle DEFG has side lengths 15 and 8, while Rectangle WXYZ has side lengths 7.5 and 4. If we divide the corresponding side lengths of WXYZ by 2, we obtain the side lengths of DEFG. This shows that the sides of the two rectangles are proportional.
Additionally, since both rectangles are right angles, their angles are equal. Therefore, we can conclude that the two rectangles are similar.