1. The problem asks to identify which two statements about perpendicularity (\(\perp\)) and parallelism (\(\parallel\)) between vectors are both true. 2. Recall the definitions: - Two vectors are perpendicular if they meet at a right angle (90 degrees). - Two vectors are parallel if they lie along the same line or in the same direction. 3. Given the graph description, we analyze each statement: - Statement 1: \(\vec{DI} \perp \vec{JG}\) and \(\vec{KF} \perp \vec{JG}\) - Statement 2: \(\vec{DI} \perp \vec{KF}\) and \(\vec{DI} \perp \vec{EH}\) - Statement 3: \(\vec{EH} \perp \vec{JG}\) and \(\vec{KF} \parallel \vec{DI}\) - Statement 4: \(\vec{EH} \perp \vec{JG}\) and \(\vec{KF} \parallel \vec{JG}\) 4. From the graph, the two lines with points D, E, F and K, J, G, H are parallel lines intersected by transversals. 5. Since \(\vec{EH} \perp \vec{JG}\) is true (given perpendicular marks at E and H), and \(\vec{KF} \parallel \vec{DI}\) is true because both lie along the same parallel line, Statement 3 is true. 6. Also, \(\vec{EH} \perp \vec{JG}\) is true, but \(\vec{KF} \parallel \vec{JG}\) is false because \(\vec{KF}\) is not parallel to \(\vec{JG}\) (one is transversal, the other is a line), so Statement 4 is false. 7. Statement 1 is false because \(\vec{DI} \perp \vec{JG}\) is false (both are on parallel lines, not perpendicular), and \(\vec{KF} \perp \vec{JG}\) is false. 8. Statement 2 is false because \(\vec{DI} \perp \vec{KF}\) is false (both on the same line), and \(\vec{DI} \perp \vec{EH}\) is false. 9. Therefore, the two statements that are both true are those in Statement 3: \(\vec{EH} \perp \vec{JG}\) and \(\vec{KF} \parallel \vec{DI}\). Final answer: Statement 3 is true.