1. 3.3, 3.6 Prove Theorems about Perpendicular Lines

2. Proving Conditional Statements (if-then) NameMathStatementTrue/False Conditional P → Q If a set of angles are a linear pair, then they are supplementary True Converse Q → P If a set of angles are supplementary, then they are a linear pair. False Inverse ~P →~Q If a set of angles are not a linear pair, then they are not supplementary False Contrapositive ~Q →~P If a set of angles are not supplementary, then they are not a linear pair. True Biconditional P↔QA set of angles are a linear pair IFF they are supplementary FALSE since Conditional and Converse not both true

3. If I know corresponding and alternate interior/exterior angles are congruent, I can prove lines are parallel.

4. Theorems/Postulates CONVERSE Converse of Corresponding Angles Postulate: –If 2 lines are cut by a transversal, and a pair of corresponding angles are congruent, then the 2 lines are parallel THEOREMS: If two lines are cut by a transversal and a pair of – alternate interior angles are congruent, then the lines are parallel – alternate exterior angles are congruent, then the lines are parallel –consecutive interior angles are supplementary, then the lines are parallel

5. Transitive Property of Lines

6. Parallel Lines Properties

7. Piecing it Together

9. Two Column Proof

10. Paragraph Proof

12. Conclusion: Two lines are cut by a transversal. How can you prove the lines are parallel? Show that either a pair of alternate interior angles, a pair of corresponding angles, or a pair of alternate exterior angles is congruent, or show that a pair of consecutive interior angles is supplementary. Write 3 bi-conditional Statements using the theorems we discussed today

13. Coordinate Proof 1) Prove that quadrilateral A(1,2), B(2,5), C(5,7) and D(4,4) is a parallelogram by using slopes. Prove that A(1,1), B(4,4), C(6,2) are the vertices of a right triangle. 5) Prove that A(-3,2), B(-2,6), C(2,7) and D(1,3) is a rhombus. Prove that A(4,-1), B(5,6), C(1,3) is an isosceles right triangle.

14. Perpendicular Problems

15. Perpendicular Discussion Perpendicular and Linear Pairs Perpendicular Lines and Angles Formed Adjacent Acute Angles and Perpendicular Lines Transversal perpendicular to 1 line in a set of parallel lines Lines perpendicular to the same line

16. Congruent Angles Linear Pairs

18. Perpendicular Lines Right Angles

19. Adjacent Acute Angles

20. Perpendicular Transversal Theorem

21. Lines Parallel to a Transversal Theorem