Question

refer to the diagram shown. if $overline{ab}paralleloverline{cd}$, the sss theorem can be used to show that $\triangle acdcong\triangle cab$.

Explanation:

Step1: Identify common side

In $\triangle ACD$ and $\triangle CAB$, $AC = AC$ (common side).

Step2: Use parallel - side property

Since $\overline{AB}\parallel\overline{CD}$, $AB = CD$ (opposite sides of a parallelogram, and if one - pair of opposite sides is parallel and equal, the figure can be considered in terms of congruence). Also, $AD = CB$ (opposite sides of a parallelogram or based on the parallel - side relationship and properties of the figure).

Step3: Apply SSS theorem

By the Side - Side - Side (SSS) congruence theorem, which states that if three sides of one triangle are equal to three corresponding sides of another triangle, the two triangles are congruent. Here, in $\triangle ACD$ and $\triangle CAB$, $AC = AC$, $AB = CD$, $AD = CB$, so $\triangle ACD\cong\triangle CAB$.

Answer:

The SSS theorem is correctly used to show that $\triangle ACD\cong\triangle CAB$.