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.
[list=1][*]If 2 parallelograms have all 4 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 doesn’t work.[/*][/list]
In parallelograms [i]ABCD[/i] and [i]EFGH[/i], [br][math]\overline{AB}\cong\overline{EF}[/math][br][math]\overline{BC}\cong\left|\overline{FG}\right|[/math][br][math]\angle ABC\cong\angle EFG[/math]
Are [i]ABCD[/i] and [i]EFGH[/i] congruent?[br][br]If so, explain your reasoning. If not, use the tools available to show that it doesn't work.
IM G Unit 2 Lesson 15 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/2/15/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].