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Download 3.7 (Day 2) Discovering Properties of Parallel Lines
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Transcript
3.7 (Day 2) Discovering Properties of Parallel Lines Objective: To use properties of parallel lines to find angle measures and to identify parallel lines. C-16: Corresponding Angles Conjecture: If two parallel lines are cut by a transversal, then corresponding angles are ___________________ Converse of the Corresponding Angles Conjecture: If two lines are cut by a transversal forming pairs of corresponding angles that are congruent, then the lines are _________________________ C-17: Alternate Interior Angles Conjecture: If two parallel lines are cut by a transversal, then alternate interior angles are ___________________ Converse of the Alternate Interior Angles Conjecture: If two lines are cut by a transversal forming pairs of alternate interior angles that are congruent, then the lines are _________________________ C-18: Alternate Exterior Angles Conjecture: If two parallel lines are cut by a transversal, then alternate exterior angles are ___________________ Converse of the Alternate Exterior Angles Conjecture: If two lines are cut by a transversal forming pairs of alternate exterior angles that are congruent, then the lines are _________________________ C-19: Same-Side Interior Angles Conjecture: If two parallel lines are cut by a transversal, then same-side interior angles are _______________________ Converse of the Same-Side Interior Angles Conjecture: If two lines are cut by a transversal forming pairs of same-side interior angles that are supplementary, then the lines are _________________________ C-20: Same-Side Exterior Angles Conjecture: If two parallel lines are cut by a transversal, then same-side exterior angles are _______________________ Converse of the Same-Side Exterior Angles Conjecture: If two lines are cut by a transversal forming pairs of same-side exterior angles that are supplementary, then the lines are _________________________ Examples: Find the value of each variable. (Use new conjectures) 1. 2. 3. Find the measure of each numbered angle. (Use new conjectures) 4. *5. Examples: (Use new converses) 6. Is 𝑎 ∥ 𝑏? *Use vertical angles or linear pairs. 7. Is quadrilateral ABCD a parallelogram? *Recall: A parallelogram has ____ pairs of parallel sides. Yes or No (circle one) _______ ∥ _______ _______ ∥ _______ Algebra: Use new conjectures or converses. 8. Find the value of x. 9. Find the value of x. 10. What value of x would make 𝑙 ∥ 𝑚?
