1. **State the problem:** We have parallelogram JKLM reflected across the y-axis and then translated down 6 units to form parallelogram QRST. We need to determine which statements about angles and sides are true. 2. **Understand the transformations:** - Reflection across the y-axis changes a point $(x,y)$ to $(-x,y)$. - Translation down 6 units changes a point $(x,y)$ to $(x,y-6)$. 3. **Find coordinates of JKLM vertices:** Given approximate coordinates: - $J(-6,6)$ - $K(-4,6)$ - $L(-2,2)$ - $M(-6,2)$ 4. **Apply reflection across y-axis:** - $J' = (6,6)$ - $K' = (4,6)$ - $L' = (2,2)$ - $M' = (6,2)$ 5. **Apply translation down 6 units:** - $J'' = (6,6-6) = (6,0)$ - $K'' = (4,6-6) = (4,0)$ - $L'' = (2,2-6) = (2,-4)$ - $M'' = (6,2-6) = (6,-4)$ 6. **Compare with QRST vertices given:** - $Q(6,-2)$ - $R(2,-2)$ - $S(4,-8)$ - $T(6,-8)$ The transformed points do not exactly match QRST vertices, so the problem's given QRST vertices are slightly different, but the transformation is as described. 7. **Check statements:** **A. Angle K has the same measure as angle Q.** - Reflection and translation are rigid motions preserving angle measures. - Therefore, angle $K$ in JKLM corresponds to angle $Q$ in QRST and they are congruent. **B. Angles M and T are congruent.** - Angle $M$ in JKLM corresponds to angle $T$ in QRST after the transformations. - Since transformations preserve angles, angles $M$ and $T$ are congruent. **C. Side JK is the same length as side QT.** - Side $JK$ length: $$ JK = \sqrt{(-4 + 6)^2 + (6 - 6)^2} = \sqrt{2^2 + 0^2} = 2 $$ - Side $QT$ length: $$ QT = \sqrt{(6 - 6)^2 + (-2 + 8)^2} = \sqrt{0^2 + 6^2} = 6 $$ - Since $2 \neq 6$, side $JK$ is not the same length as side $QT$. **Final answers:** - A is true. - B is true. - C is false.