Question

the four - sided geometric figure pictured is called a parallelogram. one feature of parallelograms is that opposite sides have equal lengths. the dotted line splits the parallelogram into two triangles. what is true about the congruency of the two triangles? more information is needed. the triangles can be proven congruent using sss. the triangles can be proven congruent using hl. the triangles are not congruent.

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite sides are equal. Let the parallelogram be \(ABCD\) and the dotted - line be a diagonal, say \(AC\). We have \(AB = CD\) and \(AD=BC\). Also, the diagonal \(AC\) is common to both \(\triangle ABC\) and \(\triangle CDA\).

Step2: Apply congruence criterion

We have three pairs of equal sides: \(AB = CD\), \(BC = DA\), and \(AC=CA\). By the Side - Side - Side (SSS) congruence criterion, \(\triangle ABC\cong\triangle CDA\).

Answer:

The triangles can be proven congruent using SSS.