Does SSSS (four sides of one are congruent to four sides of the other) work as a congruence theorem (a way to prove they are congruent) for quadrilaterals? Explain.
The SSSS (Side-Side-Side-Side) property is not a valid congruence theorem for quadrilaterals. It is important to note that congruence theorems are specific to certain types of geometric figures, and quadrilaterals have their own set of congruence theorems.
Quadrilaterals can be proven congruent using different methods depending on their properties. The two most commonly used congruence theorems for quadrilaterals are SSS (Side-Side-Side) and SAS (Side-Angle-Side).
SSS (Side-Side-Side) Congruence Theorem: For two quadrilaterals to be congruent, all four sides of one quadrilateral must be congruent to the corresponding four sides of the other quadrilateral.
SAS (Side-Angle-Side) Congruence Theorem: For two quadrilaterals to be congruent, two pairs of corresponding sides must be congruent, and the included angles between these sides must be congruent.
So, when proving congruence for quadrilaterals, you would typically use SSS or SAS notations, rather than the four S's as seen in triangles.
To explicitly prove the congruence of two quadrilaterals, you would need to identify and compare corresponding sides and angles. By showing that all corresponding sides and angles are congruent according to either the SSS or SAS criteria, you can establish the congruence of the two quadrilaterals.