Question

bc⊥ae af = bf prove: ac = bd which of the following is not a reason used in this proof? definition of perpendicular. vertical angles are equal. reflexive

Explanation:

• Step 2: Since \(AD\perp AE\) and \(BC\perp AE\) (given), by the definition of perpendicular (if two lines are perpendicular, the angles formed are right angles), \(\angle C\) and \(\angle D\) are right angles.
• Step 3: \(\angle AFC\) and \(\angle BFD\) are vertical angles. By the property that vertical angles are equal, \(\angle AFC=\angle BFD\).
• Step 4: We have \(AF = BF\) (given), \(\angle C=\angle D = 90^{\circ}\) (from step 2), \(\angle AFC=\angle BFD\) (from step 3). So, by the AAS (Angle - Angle - Side) congruence criterion, \(\triangle AFC\cong\triangle BFD\).
• Step 5: If two triangles are congruent, their corresponding sides are equal. So, \(AC = BD\) (corresponding parts of congruent triangles).

The reflexive property (\(a=a\)) is not used in this proof. The definition of perpendicular is used in step 2 (to get right angles) and the vertical - angles - are - equal property is used in step 3.

Answer:

Reflexive.