Question

statements reasons 1 \\(\overline{ab} \cong \overline{cd}, \overline{ad} \cong \overline{bc}\\) 1 given 2 \\(\overline{ac} \cong \overline{ac}\\) 2 reflexive property 3 \\(\triangle adc \cong \triangle cba\\) 3 ? 4 \\(\angle dac \cong \angle bca, \angle acd \cong \angle cab\\) 4 cpctc 5 \\(\angle dac\\) and \\(\angle bca\\) are alt. int. \\(\angle s\\), \\(\angle acd\\) and \\(\angle cab\\) are alt. int. \\(\angle s\\) 5 definition of alternate interior angles 6 \\(\overline{ab} \parallel \overline{cd}, \overline{ad} \parallel \overline{bc}\\) 6 converse of the alternate interior angles theorem 7 (abcd) is a parallelogram 7 definition of parallelogram what is the missing reason in step 3? \\(\bigcirc\\) triangle angle sum theorem \\(\bigcirc\\) sas congruency theorem \\(\bigcirc\\) sss congruency theorem \\(\bigcirc\\) cpctc

Explanation:

Step1: Analyze the given congruent sides

We are given \(AB\cong CD\), \(AD\cong BC\), and \(AC\cong AC\) (reflexive property).

Step2: Recall triangle congruence theorems

The SSS (Side - Side - Side) congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
In \(\triangle ADC\) and \(\triangle CBA\), we have \(AD = BC\), \(DC = BA\), and \(AC=CA\).

Answer:

SSS congruency theorem