3-4 Parallel and Perpendicular lines Students will make conjectures about the measure or congruence of angles and build a progression of logical statements (i.e. a proof) using their knowledge of the intersections of parallel and perpendicular lines. 3-4 Parallel and Perpendicular lines To relate parallel and perpendicular lines.

Be sure to record your total on the portfolio sheet. 3-4 Quiz The following questions are to help you decide if you understood today’s lesson. Please take time to see me if you do not get at least 2 questions right. Be sure to record your total on the portfolio sheet.

1. Each tie on the railroad tracks is perpendicular to both of the tracks. What is the relationship between the two tracks? Justify your answer. The two tracks are perpendicular by the definition of complementary angles. The two tracks are parallel by the Same-Side Interior Angles Postulate. The two tracks are perpendicular by the Perpendicular Transversal Theorem. The two tracks are parallel by the Converse of the Perpendicular Transversal Theorem. Non-Response Grid

2. Each sheet of metal on a roof is perpendicular to the top line of the roof. What can you conclude about the relationship between the sheets of roofing? Justify your answer. The sheets of metal are all parallel to each other by the Transitive Property of Parallel Lines. The sheets of metal are all parallel to each other because in a plane, if two lines are perpendicular to the same line, then they are parallel to each other. The sheets of metal are all parallel to each other because in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other. The sheets of metal are all parallel to each other by the Alternate Interior Angles Theorem. Non-Response Grid

𝑎∥𝑏, by the Perpendicular Transversal Theorem 3. If 𝑐⊥𝑏 and 𝑎∥𝑐 , what do you know about the relationship between lines a and b? Justify your conclusion with a theorem or postulate. 𝑎∥𝑏, by the Perpendicular Transversal Theorem 𝑎⊥𝑏, by the Alternate Exterior Angles Theorem 𝑎⊥𝑏, by the Perpendicular Transversal Theorem not enough information Non-Response Grid

No. The angles for each corner form a 89° angle. 4. A carpenter cut the top section of window frame with a 42° angle on each end. The side pieces each have a 47° angle cut at their top end, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to scale. No. The angles for each corner form a 89° angle. Yes. The angles at each corner form a 90° angle. Yes. The angles at each corner are supplementary. Yes. Two lines perpendicular to the same line are parallel. Non-Response Grid

5. In a plane, line k is parallel to line l and line j is perpendicular to line l. What can you conclude about the relationship between lines j and k? Lines j and k are parallel. Lines j and k are skew. Lines j and k are the same line. Lines j and k are perpendicular. Non-Response Grid

Assignment 3-4 p. 167 -168 #6-24 even Then rate your assignment 4-3-2-1-0 as to how well you understood the lesson and write why you rated yourself that way.