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CP Geometry 11/03/15 Name: ________________________________ Angle Relationships Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles is ______congruent_______________. Sketch: Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles is _______congruent___________. Sketch: Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is ____supplementary______. Sketch: Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is ______congruent_________. Sketch: Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is ___perpendicular_________ to the other. Sketch: Converse of Corresponding Angles Postulate If two lines are cut by a transversal so the corresponding angles are _congruent___ then the lines are __parallel_____. Sketch: Alternate Exterior Angles Converse If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is ___congruent__, then the two lines are _____parallel_____. Sketch: Consecutive Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is ___supplementary___, then the lines are _____parallel_______. Sketch: Alternate Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is ____congruent____, then the lines are ____parallel_________. Sketch: Perpendicular Transversal Converse In a plane, if two lines are perpendicular to the same line, then they are ___parallel_______. Sketch: Given: j || k and j || l Prove: k || l j || k and j || l given ∠1 ≅ ∠ 2 ∠ 1 ≅ ∠ 3 ∠ 2 ≅ ∠ 3 if lines ||, corr ∠’s ≅ if line ||, corr ∠’s ≅ if corr ∠’s ≅ , then lines are || € € € € € € € € € € € € € € € Given: j || k, ∠1 ≅ ∠2 Prove: m || n € j || k, ∠1 ≅ ∠2 given ∠ 2 ≅ ∠4 € ∠1 ≅ ∠ 4 if lines ||, then alternate interior angles are ≅ substitution if corr angles ≅ , then the lines are || m || n € € € € € € € €
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