1. The problem asks if any additional information is needed to show that triangles $\triangle DEF$ and $\triangle GHJ$ are congruent by SAS (Side-Angle-Side). 2. SAS congruence requires two pairs of corresponding sides and the included angle between them to be equal. 3. To confirm $\triangle DEF \cong \triangle GHJ$ by SAS, we need to verify: - Two pairs of sides are equal in length. - The angle between those sides in one triangle equals the corresponding angle in the other. 4. Given angles: $m\angle D = 4x^\circ$, $m\angle H = (2x+1)^\circ$, $m\angle F = 75^\circ$, and $m\angle E = m\angle H = (2x+1)^\circ$. 5. Since $m\angle E = m\angle H$, and $m\angle F = 75^\circ$, we can use the triangle angle sum property: $$m\angle D + m\angle E + m\angle F = 180^\circ$$ Substitute the values: $$4x + (2x+1) + 75 = 180$$ 6. Simplify the equation: $$4x + 2x + 1 + 75 = 180$$ $$6x + 76 = 180$$ 7. Subtract 76 from both sides: $$6x + \cancel{76} - \cancel{76} = 180 - 76$$ $$6x = 104$$ 8. Divide both sides by 6: $$\frac{6x}{\cancel{6}} = \frac{104}{\cancel{6}}$$ $$x = \frac{104}{6} = 17.3$$ 9. Therefore, $x = 17.3$ degrees. 10. With $x$ found, angles $m\angle D = 4(17.3) = 69.2^\circ$ and $m\angle H = 2(17.3) + 1 = 35.6^\circ$ approximately. 11. To conclude SAS congruence, we must confirm the two pairs of sides including these angles are equal, which is not provided here. 12. Hence, additional side length information is needed to confirm $\triangle DEF \cong \triangle GHJ$ by SAS.