You have a new neighbor move in across the street from where your house is now located after the flood. They build the same exact house as you have. Is your neighbor’s house congruent to your house? Explain your answer.
No, my neighbor's house is not congruent to my house. Congruence refers to two figures that have the same shape and size. While the two houses may have the same shape, they do not have the same size because my house has been affected by the flood. Therefore, our houses are not congruent.
If the house is a reflection of my house in chapter 2 over the x-axis would it be congruent?
Yes, if your neighbor's house is a reflection of your house in Chapter 2 over the x-axis, then their house would be congruent to yours. Reflection is a type of transformation that preserves the shape and size of the figure. In this case, the reflection over the x-axis would result in the same shape and size of your house, making them congruent.
if my house is rotated 180 degrees counterclockwise, would it still be congruent to my neighbor's house if their house was left untouched?
Yes, if your house is rotated 180 degrees counterclockwise, it would still be congruent to your neighbor's house if their house was left untouched. A 180-degree rotation is a transformation that preserves both the shape and the size of the figure. Therefore, even though the orientation of the houses would be different, the shapes and sizes of the houses remain the same, making them congruent.
