Question

triangle proofs
complete the proof above by ordering the reasons below:
show your thinking

Explanation:

Step1: Alternate - interior angles

Since \(ABDC\) is a parallelogram, \(AB\parallel CD\), so \(\angle BAC=\angle DCE\) (alternate - interior angles).

Step2: Opposite sides of parallelogram

In parallelogram \(ABDC\), \(AB = CD\) (opposite sides of a parallelogram are equal).

Step3: Definition of mid - point

\(C\) is the mid - point of \(AE\), so \(AC=EC\).

Step4: Side - Angle - Side (SAS)

With \(AB = CD\), \(\angle BAC=\angle DCE\), and \(AC = EC\), \(\triangle ABC\cong\triangle CDE\) by SAS congruence criterion.

Answer:

1. Alternate - interior angles; 2. Opposite sides of parallelogram; 3. Definition of mid - point; 4. Side - Angle - Side (SAS)