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 properties of parallelogram

In a parallelogram, opposite sides are equal. Let the parallelogram be \(ABCD\) with \(AB = CD\) and \(AD=BC\). The dotted line (say diagonal \(AC\)) divides the parallelogram into \(\triangle ABC\) and \(\triangle ADC\).

Step2: Apply SSS (Side - Side - Side) congruence criterion

For \(\triangle ABC\) and \(\triangle ADC\), we have \(AB = CD\) (opposite sides of parallelogram), \(AD = BC\) (opposite sides of parallelogram), and \(AC=AC\) (common side). By SSS (\(AB = CD\), \(AD = BC\), \(AC = AC\)), \(\triangle ABC\cong\triangle ADC\).
HL (Hypotenuse - Leg) is used for right - angled triangles. Since we have no information about right angles, HL is not applicable. And we do not need more information as we can use the properties of parallelogram and SSS.

Answer:

The triangles can be proven congruent using SSS.