Definition of Congruence Two geometric figures are congruent

Definition of Congruence Two geometric figures are congruent if a composition of a finite number of rigid motions maps one to the other. Informally, two congruent figures are the same size and shape. However, this is not a definition of congruence. 1/25/2022 Algebra 1 Institute 1

Congruence of Triangles • Because rigid motions preserve distance and angles, two congruent triangles necessarily have three pairs of congruent sides and three pairs of congruent angles. • The converse is also true: two triangles with three pairs of equal sides and three pairs of equal angles are congruent. • With triangles, instead of requiring six sets of conditions to guarantee triangle congruence, a judicious choice of three sets of conditions is sufficient. 1/25/2022 Algebra 1 Institute 2

Congruence of Triangles Theorems allow us to infer congruence when fewer than 6 conditions are satisfied. 1/25/2022 Algebra 1 Institute 3

Best Known Theorems • SAS - If two triangles have a pair of equal angles and corresponding sides of these angles in the triangle are pairwise equal, then the two triangles are congruent. • ASA - If two triangles have two pairs of equal angles and the common side of the angles in one triangle is equal to the corresponding side in the other triangle, then the triangles are congruent. • SSS -If two triangles have three pairs of equal sides, then they are congruent. 1/25/2022 Algebra 1 Institute 4

Patty Paper Investigation In your group, follow the instructions given in the participants handout (the third page after the third green divider…the second page one in that section) 1/25/2022 Algebra 1 Institute 5

Proof of ASA by Basic Rigid Motions 1/25/2022 Algebra 1 Institute 6

Now it’s your turn… SSS SAA HL 1/25/2022 Algebra 1 Institute 7