In a plane, if a transversal is Perpendicular Perpendicular perpendicular to one of 2 Transversal Transversal parallel lines, then it is parallel Theorem perpendicular to the other. If 2 coplanar lines are Perpendicular perpendicular to the same 3-4-3 Parallel line, then the 2 lines are parallel to each other. Chapter 4 Properties, Postulates and Theorems Congruent Triangles Postulate or What it says Sketch Theorem Name Triangle Sum The sum of the angle measures of Theorem a triangle is 180°. (4-2-1) 4-2 Exterior Angle The measure of an exterior angle is equal to Theorem the sum of its 2 remote interior angles. Third Angles If two angles of one triangle are congruent to Theorem two angles of another triangle, then the third (4-2-5) pair of angles are congruent. Ways to prove that 2 triangles are congruent Side-Side-Side If three sides of one triangle are congruent (SSS) to three sides of another triangle, THEN Congruence THE TRIANGLES ARE CONGRENT. 4-4 If two sides and the included angle of one Side-Angle-Side triangle are congruent to two sides and the (SAS) included angle of another triangle, THEN Congruence THE TRIANGLES ARE CONGRENT.
Perpendicular Transversal Theorem In a plane, if a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other. Perpendicular Transversal parallel 3-4-3 If 2 coplanar lines are perpendicular to the same line, then the 2 lines are parallel to each other. Perpendicular Parallel Chapter 4 Properties, Postulates and Theorems Congruent Triangles Postulate or Theorem Name What it says Sketch 4-2 Triangle Sum Theorem (4-2-1) The sum of the angle measures of a triangle is 180°. Exterior Angle Theorem The measure of an exterior angle is equal to the sum of its 2 remote interior angles. Third Angles Theorem (4-2-5) If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. Ways to prove that 2 triangles are congruent 4-4 Side-Side-Side (SSS) Congruence If three sides of one triangle are congruent to three sides of another triangle, THEN THE TRIANGLES ARE CONGRENT. Side-Angle-Side (SAS) Congruence If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, THEN THE TRIANGLES ARE CONGRENT.
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