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Lesson 2.1.4B Resource Page Theorem Graphic Organizer Key These converses were proved in Lesson 2.1.4: same-side interior angles supplementary ➙ lines are parallel (problem 2-35) corresponding angles congruent ➙ lines are parallel (problem 2-38) alternate interior angles congruent ➙ lines are parallel (problem 2-38) These converses were proved previously: leg2 + leg2 = hypotenuse2 ➙ right triangle (previous course) ≅ parts ➙ ≅ Δs (previous course) This converse of a theorem is not true: two angles congruent ➙ vertical angles These converses of theorems can be proved using Δs ≅➙ ≅ parts: Triangles congruent ➙ all three pairs of corresponding sides are congruent (SSS ≅). Triangles congruent ➙ two pairs of corresponding sides are congruent and the angles between them (the included angle) are congruent (SAS ≅). Triangles congruent ➙ two angles and the side between them are congruent to the corresponding angles and side in the other triangle (ASA ≅). Triangles congruent ➙ two pairs of corresponding angles and a pair of corresponding sides that are not between them are congruent (AAS ≅). Triangles congruent ➙ the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle (HL ≅). © 2015 CPM Educational Program. All rights reserved. Core Connections Integrated II