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?
the triangles can be proven congruent using hl.
the triangles are not congruent.
the triangles can be proven congruent using sss.
more information is needed.

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite sides are equal, and the diagonal is a common side for both triangles. So, for the two triangles formed by the diagonal: side 1 (of triangle 1) = side 1 (of triangle 2) (opposite sides of parallelogram), side 2 (of triangle 1) = side 2 (of triangle 2) (opposite sides of parallelogram), and the diagonal is common (side 3 for both).

Step2: Apply SSS congruence

SSS (Side - Side - Side) congruence criterion states that if three sides of one triangle are equal to three corresponding sides of another triangle, the triangles are congruent. Here, the three sides of each triangle (two sides of the parallelogram and the diagonal) are equal. HL (Hypotenuse - Leg) is for right - angled triangles, and we don't know if these are right - angled. The triangles are congruent, so the options "The triangles are not congruent" and "More information is needed" are wrong. So the triangles can be proven congruent using SSS.

Answer:

The triangles can be proven congruent using SSS.