Question

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Explanation:

Step1: Analyze Given Information

We know \(\overline{AB} \perp \overline{BC}\) and \(\overline{DE} \perp \overline{BC}\) (given). Also, we have to use the boxed terms: perpendicular, \(\overline{DE} \perp \overline{BC}\), \(\angle ABC \cong \angle DEC\), Angle - Angle, \(\angle C \cong \angle C\).

Step2: Fill Statement 1's Second Part

Since we are given two perpendiculars, the second statement under 1 should be \(\overline{DE} \perp \overline{BC}\) (as it's part of the given info for the proof).

Step3: Reason for Statement 2

The reason for \(\angle ABC\) and \(\angle DEC\) being right angles is the definition of perpendicular line segments (since perpendicular lines form right angles).

Step4: Statement 3

By "All right angles are congruent", the statement here is \(\angle ABC \cong \angle DEC\) (as both are right angles).

Step5: Statement 4

By "Reflexive Property", the angle that is congruent to itself is \(\angle C \cong \angle C\).

Step6: Reason for Statement 5

The similarity postulate used when two angles are congruent is the Angle - Angle (AA) Similarity Postulate, so the reason is Angle - Angle.

Answer:

1. Second part of Statement 1: \(\boldsymbol{\overline{DE} \perp \overline{BC}}\)
2. Reason for Statement 2: \(\boldsymbol{\text{perpendicular}}\)
3. Statement 3: \(\boldsymbol{\angle ABC \cong \angle DEC}\)
4. Statement 4: \(\boldsymbol{\angle C \cong \angle C}\)
5. Reason for Statement 5: \(\boldsymbol{\text{Angle - Angle}}\)