IM Geo.2.15 Lesson: Congruence for Quadrilaterals
Given that ABCD is a parallelogram.
What must be true?
What could possibly be true?
What definitely canāt be true?
Jada is learning about the triangle congruence theorems: Side-Side-Side, Angle-Side-Angle, and Side-Angle-Side. She wonders if there are any theorems like these for parallelograms.
If 2Ā parallelograms have all 4Ā pairs of corresponding sides congruent, do the parallelograms have to be congruent? If so, explain your reasoning. If not, use the tools available to show that it doesnāt work.
In parallelogramsĀ Ā andĀ , segmentĀ Ā is congruent to segmentĀ , segmentĀ Ā is congruent to segmentĀ , and angleĀ Ā is congruent to angleĀ . AreĀ Ā andĀ Ā congruent? If so, explain your reasoning. If not, use the tools available to show that it doesnāt work.
Come up with another criteria that is enough to be sure that 2 parallelograms are congruent.
Try to use as few measurements as you can. Be prepared to convince others that your shortcut works.
Will your rule work for any quadrilateral, not just parallelograms?
If it does, justify your rule. If it doesn't, adjust your rule so it works for any quadrilateral and justify your new rule.