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Definitions, Properties and Theorems as Conditionals If a segment bisects another segment, Definition of segment bisector then it intersects at its midpoint. If a point is a midpoint, then it divides a segment into 2 segments. Definition of midpoint , If Definition of congruent segments . then , If Definition of congruent angles . then If two lines are perpendicular, Definition of perpendicular lines then they form right angles. If two lines form right angles, Definition of perpendicular lines then they are perpendicular. If an angle is right, Definition of right angle then its measure is 90. If an angle’s measure is 90, Definition of right angle then it is a right angle. If a ray bisects an angle, Definition of angle bisector then it forms 2 angles. If B A C Segment Addition Postulate then If . R A B C Angle Addition Postulate then . If a triangle is isosceles, then it has at least 2 sides. If a triangle has at least 2 sides, then it is isosceles. Definition of isosceles triangle Definition of isosceles triangle If two angles are right angles, then they are congruent. If A All right angles are congruent. B Reflexive Property of Congruence then . If and then If . 1 Transitive Property of Congruence 2 then 1 2. If two lines are parallel and cut by a transversal, Vertical Angles Theorem Alternate Interior Angles Theorem then alternate interior angles are congruent. If alternate interior angles are congruent, then the lines are parallel. Converse of the Alternate Interior Angles Theorem If corresponding parts of polygons are , then the polygons are congruent If two triangles are congruent, then corresponding parts are congruent. If three sides of one triangle are congruent to three sides of another triangle, Definition of congruent polygons CPCTC SSS Postulate then the triangles are congruent. If 2 sides & the included angle of one triangle are congruent to 2 sides & the included angle of another triangle, SAS Postulate then the triangles are congruent. If 2 angles & the included side of one triangle are congruent to 2 angles & the included side of another triangle, ASA Postulate then the triangles are congruent. If 2 angles & the nonincluded side of one triangle are congruent to 2 angles & the nonincluded side of another triangle , AAS Theorem then the triangles are congruent. If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of a another right triangle, HL Theorem then the triangles are congruent. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are . Third Angle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are . If two angles of a triangle are congruent, then the sides opposite those angles are . Isosceles Triangle Theorem Converse of the Isosceles Triangle Theorem