Question

proving a quadrilateral is a parallelogram
given: ( overline{ab}congoverline{cd} ) and ( overline{ad}congoverline{bc} )
prove: ( abcd ) is a parallelogram
what is the missing reason in step 3?
sss congruency theorem
sas congruency theorem
triangle angle sum theorem
cpctc

Explanation:

Step1: Recall congruence theorems

We have \(AD\cong CD\), \(AD\cong BC\) (given) and \(AC = AC\) (reflexive property).

Step2: Apply SSS congruency theorem

In \(\triangle ADC\) and \(\triangle CBA\), since \(AD\cong CB\), \(CD\cong AB\), \(AC\cong AC\), by the Side - Side - Side (SSS) congruency theorem, \(\triangle ADC\cong\triangle CBA\).

Answer:

SSS congruency theorem