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Tyiana Combs Geo 1 Objective ~ To use a transversal in proving parallel lines Vocabulary Flow Proof ~ a proof is a convincing argument that uses deductive reasoning. A form of a proof is a flow proof in which arrows show the logical connections between the statements. Example of a Flow Proof (for the HL Theorem) Postulate 3-2 Converse of the Corresponding Angles Postulate If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. Theorem 3-5 Converse of the Alternative Interior Angles Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. If angle 1 is congruent to angle 2, then l is parallel to m. Theorem 3-5 Converse of the Alternative Interior Angles Theorem If two lines a transversal alternate interiorAngles angles Theorem that are congruent, then the two Theorem 3-6 and Converse of the form Same-Side Interior are parallel. If angle 1 isform congruent to angle 2, then l is parallel m. If lines two lines and a transversal same-side interior angles that aretosupplementary, then the two lines are parallel. If angle 4 is congruent to angle 5, then l is parallel to m. Theorem 3-7 Converse of the Alternative Exterior Angles Theorem If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel. If angle 1 is congruent to angle 7, then l is parallel to m. Theorem 3-8 Converse of the Same-Side Exterior Angles Theorem If two lines and a transversal form same-side exterior angles that are supplementary, then the two lines are parallel. If angle 1 is congruent to angle 4, then l is parallel to m. 1. Make a proof for Theorem 3-5. Given: Angle 1 is congruent to Angle 2. Prove: l is parallel to m. 2. Which lines, if any (using the diagram shown in Theorem 3-6), must be parallel if Angle 1 is congruent to Angle 5? 3. Find the value of x for which l is parallel to m. 40• (2x+6) 4. Which lines or segments are parallel? Justify your answer. C B E G 5. Fill in the blanks and name the theorem: If two lines and a transversal form same-side __________ angles that are _______________, then the two lines are _________. If angle 4 is congruent to angle 5, then l is parallel to m. 1. Theorem 3-5 Statements Reasons Angle 1 is congruent Given to Angle 2 Angle 1 is congruent Vertical angles are congruent to Angle 3 Angle 3 is congruent Transitive Property of Congruence to Angle 2 l is parallel to m Corresponding angles are congruent 2. Line l and Line m. 3. 2x + 6 = 40 2x = 34 Subtract 6 from each side. x = 17 Divide each side by 2. 4. Line BE is parallel to Line CG using the Converse of Corresponding Angles Postulate. 5. Converse of the Same-Side Interior Angles Theorem If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. If angle 4 is congruent to angle 5, then l is parallel to m.