Prove Like This: Parallelogram Properties

Drag the points around. Do any things appear to always be congruent? Under what conditions will triangles ABC and CDA be congruent?

Given: ABCD is a trapezoid with AB||DC. Drag the points around. Do any things appear to always be congruent? Under what conditions will triangles ABC and CDA be congruent?

Given: ABCD is a parallelogram. Drag the points around. Do any things appear to always be congruent? Under what conditions will triangles ABC and CDA be congruent?