Question

select a term for each blank box to complete the proof showing that (\triangle abccong\triangle cda). (\triangle abccong\triangle cda) by the ______ congruence theorem. aas sas asa

Explanation:

Step1: Recall the properties of the figure

Since it is a parallelogram - like figure (implied by the markings of equal sides and parallel sides). In a parallelogram, \(AB = CD\) (marked as equal), \(AD=BC\) (not directly relevant here), and \(\angle BAC=\angle DCA\) (alternate - interior angles as \(AB\parallel CD\) and \(AC\) is a transversal). Also, \(AC\) is a common side.

Step2: Apply the congruence theorem

For \(\triangle ABC\) and \(\triangle CDA\), we have \(AB = CD\) (side), \(\angle BAC=\angle DCA\) (angle), and \(AC = CA\) (common side). By the Side - Angle - Side (SAS) congruence theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Answer:

SAS