Question

the graph shows quadrilaterals fghi and lmno. is fghi congruent to lmno? justify your answer. yes, because a translation right 12 units maps fghi onto lmno. yes, because a reflection across the y - axis maps fghi onto lmno. no, because (overline{fg}) and (overline{lm}) do not have the same length. no, because (angle h) and (angle n) do not have the same measure.

Explanation:

Step1: Recall congruence criteria

Two polygons are congruent if all corresponding sides and angles are equal.

Step2: Check side - length comparison

We can use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the lengths of corresponding sides. For example, for side $\overline{FG}$ and $\overline{LM}$. If we count the grid - squares, we can see that the lengths of corresponding sides are not the same. If the lengths of corresponding sides are not equal, the quadrilaterals are not congruent.

Step3: Analyze given options

A translation or reflection would map congruent figures onto each other. But since the side - lengths are different, these transformations won't work. And we don't have enough information to easily compare angles $\angle H$ and $\angle N$ just by looking at the graph, while side - length comparison is more straightforward.

Answer:

No, because $\overline{FG}$ and $\overline{LM}$ do not have the same length.