Question

1. how could you use parallel lines to compare figures n and m? explain your reasoning.
2. figure ghij is a reflection of figure wxyz. decide if each statement describing the sides of the figures is true or false. choose true or false for each statement.

a. $overline{gh}$ corresponds to $overline{xy}$.
b. $overline{jg}$ corresponds to $overline{zw}$.
c. $overline{ji}$ corresponds to $overline{zy}$.
d. $overline{hi}$ corresponds to $overline{xw}$.
e. $overline{hi}$ corresponds to $overline{xy}$.

Explanation:

Step1: Understand reflection properties

In a reflection, corresponding sides of the original and reflected figures have the same length and orientation relative to the reflection - axis.

Step2: Analyze each statement

• a. $\overline{GH}$ corresponds to $\overline{XY}$. By observing the orientation and position of the sides in the reflected figures, we can see that $\overline{GH}$ and $\overline{XY}$ are not corresponding sides. So it's False.
• b. $\overline{JG}$ corresponds to $\overline{ZW}$. By checking the order and position of vertices in the reflection, we find that $\overline{JG}$ and $\overline{ZW}$ are corresponding sides. So it's True.
• c. $\overline{JI}$ corresponds to $\overline{ZY}$. By looking at the figures, we can tell that $\overline{JI}$ and $\overline{ZY}$ are corresponding sides. So it's True.
• d. $\overline{HI}$ corresponds to $\overline{XW}$. By examining the orientation and position of the sides, we see that $\overline{HI}$ and $\overline{XW}$ are not corresponding sides. So it's False.
• e. $\overline{HI}$ corresponds to $\overline{XY}$. By observing the figures, we know that $\overline{HI}$ and $\overline{XY}$ are not corresponding sides. So it's False.

Answer:

a. False
b. True
c. True
d. False
e. False