Question

read the proof.
given: ( overline{ae} perp overline{ec} ; overline{bd} perp overline{dc} )
prove: ( \triangle aec sim \triangle bdc )
what is the missing statement in step 4?
( angle ace cong angle bcd )
( angle eab cong angle dbc )
( angle eac cong angle eac )
( angle cbd cong angle dbc )

Explanation:

Step1: Analyze the reflexive property

The reflexive property states that an angle is congruent to itself. In the context of proving \(\triangle AEC\sim\triangle BDC\) using the AA (Angle - Angle) similarity theorem (which requires two pairs of congruent angles), we already have \(\angle AEC\cong\angle BDC\) (right angles).

Step2: Identify the common angle

The angle \(\angle ACE\) (or \(\angle ECA\)) is the same as \(\angle BCD\) (or \(\angle DCB\)) because they are the same angle. By the reflexive property of congruence (\(\angle X\cong\angle X\)), for the angle at \(C\) in both \(\triangle AEC\) and \(\triangle BDC\), we have \(\angle ACE\cong\angle BCD\).

Answer:

\(\angle ACE\cong\angle BCD\)