Question

write a proof.
given ( c ) is the midpoint of ( overline{ae} ) and ( overline{bd} ).
prove ( \triangle abc cong \triangle edc )

Explanation:

Step1: Use the definition of midpoint

Since \(C\) is the midpoint of \(AE\), \(AC = EC\). Since \(C\) is the midpoint of \(BD\), \(BC=DC\).

Step2: Use vertical angles

\(\angle ACB\) and \(\angle ECD\) are vertical angles. So, \(\angle ACB=\angle ECD\) (vertical angles are equal).

Step3: Use the SAS (Side - Angle - Side) congruence criterion

In \(\triangle ABC\) and \(\triangle EDC\), we have \(AC = EC\), \(\angle ACB=\angle ECD\), and \(BC = DC\). By the SAS congruence criterion, \(\triangle ABC\cong\triangle EDC\).

Answer:

\(\triangle ABC\cong\triangle EDC\) (by SAS congruence criterion)