Quadrilateral [i]ABCD[/i] is a [b]parallelogram[/b].[br]By definition, that means that segment [i]AB[/i] is parallel to segment [i]CD[/i], and segment [i]BC[/i] is parallel to segment [i]AD[/i].[br][br]Constuct parallelogram [i]ABCD - Don’t forget you have tools to help you construct a parallelogram—don’t just draw something that sort of looks like a parallelogram—draw an actual parallelogram. [/i]Then draw an auxiliary line to show how [i]ABCD[/i] can be decomposed into 2 triangles.
Are the two triangles you created congruent? How do you know?
Yes, roatating 180 degrees about the midpoint of the auxiliary line would take one triangle onto another, proving they are congruent.
What conclusions can you draw about parallelograms from this diagram?
Opposite angles are congruent, opposite sides are congruent.