Question

select all true statements based on the diagram.
angle cbe is congruent to angle abe
angle ceb is congruent to angle dea
segment da is congruent to segment cb
segment dc is congruent to segment ab
line dc is parallel to line ab
line da is parallel to line cb

Explanation:

Step1: Check vertical angles

Vertical angles are congruent. $\angle CEB$ and $\angle DEA$ are vertical angles. So $\angle CEB\cong\angle DEA$.

Step2: Check congruent segments

From the diagram, there is no indication that $\angle CBE\cong\angle ABE$.
Since $DA$ and $CB$ have one tick mark each, $DA\cong CB$.
Since $DC$ and $AB$ have arrow marks (indicating parallelism, but not congruence of lengths in general trapezoid - like figures without more info, but if it's a parallelogram - from parallel arrows on $DC$ and $AB$, but the one - tick on $DA$ and $CB$ (if it's an isosceles trapezoid, $DC
ot\cong AB$ in a non - parallelogram trapezoid. Wait, no, if $DC\parallel AB$ (from arrow marks) and $DA = CB$ (tick marks), it's an isosceles trapezoid. But in general, for the given options:

• For parallel lines: The arrow marks on $DC$ and $AB$ indicate $DC\parallel AB$.
• For congruent segments: $DA\cong CB$ (tick marks).
• $\angle CEB\cong\angle DEA$ (vertical angles)

Answer:

• Angle \( CEB \) is congruent to angle \( DEA \)
• Segment \( DA \) is congruent to segment \( CB \)
• Line \( DC \) is parallel to line \( AB \)