Question

the graph shows triangles qrs and uvw. is qrs congruent to uvw? justify your answer. yes, because a rotation 180° around the origin maps qrs onto uvw. yes, because a translation left 10 units and down 12 units maps qrs onto uvw. no, because rs and vw do not have the same length. no, because ∠q and ∠u do not have the same measure.

Explanation:

Step1: Recall congruence criteria

Two triangles are congruent if all corresponding sides and angles are equal. We can check side - lengths using the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ or visually estimate and check transformations.

Step2: Analyze side - lengths

If we consider side $\overline{RS}$ and $\overline{VW}$, by counting the grid - squares (assuming each square has side - length 1), we can see that the lengths of corresponding sides are not the same. For congruent triangles, all corresponding sides must be equal.

Answer:

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