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 congruence

For \(\triangle ABC\) and \(\triangle ADC\), we have \(AB = CD\) (opposite sides of parallelogram), \(BC = AD\) (opposite sides of parallelogram), and \(AC=AC\) (common side). By SSS (Side - Side - Side) congruence criterion \(\triangle ABC\cong\triangle ADC\)

Step3: Analyze other options

• HL (Hypotenuse - Leg): HL is used for right - angled triangles. There is no information given that the triangles are right - angled.
• More information is needed: We have enough information (SSS) to prove congruence.
• Triangles are not congruent: This is false as shown by SSS congruence.

Answer:

B. The triangles can be proven congruent using SSS