1.  With your partner, answer questions 1-4 on page 575. (Questions on next slide.)  Use whatever tools seem best (available on front table).  Keep track of your answers, as well as how you solved each problem, including what tools you used and how you used them.

4. Investigation 7B Advanced Integrated Math I

9.  Work with your partner to answer page 575 #5-6

12.  Page 576 #7-10

13.  See textbook for #10

15.  You have the following tools available: ◦ Ruler ◦ Compass ◦ Protractor  You want to construct the following shapes: ◦ Circle ◦ Square ◦ Line ◦ 45° angle  Which tool(s) can you use to construct each one? Provide all possible answers.

17. Section 7.06 Advanced Integrated Math I

18.  Drawings are often rough sketches. They are aids to problem solving.  A construction is a guaranteed recipe. ◦ A construction shows how to accurately draw a figure with a specified set of tools. ◦ Constructions are solutions to problems.

19.  Compass – Any device that allows you to move a pencil a fixed distance around a point.  Straightedge – Any object with a straight edge that allows you to draw a line segment. ◦ A true straightedge does not have markings to measure distance.  Measuring Devices – Rulers and protractors  Paper – Not just a surface. Can be folded to use symmetric properties. Can be cut and rearranged.  String and tacks – Can be used to construct circles, ellipses, spirals, and other curves.

24. 1) Do you see Tony’s triangle? Explain how you know his triangle has the correct side lengths. 2) The title of this lesson is “Compasses, Angles, and Circles,” but this lesson has not yet mentioned compasses, angles, or circles. How do Sasha’s and Tony’s ruler tricks both imitate a compass? 3) How can a compass make a geometric construction easier?

25. 1. Draw a line segment. 2. Without measuring, construct its midpoint.

27.  A midpoint is the point on a segment that is halfway between the two endpoints.  Equidistant means “the same distance.”  The perpendicular bisector of a segment is the line that is perpendicular to the segment at the segment’s midpoint.

28.  Each point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.

29.  Use converse of the Perpendicular Bisector Theorem

30.  An altitude is a perpendicular segment from a vertex of a triangle to the line that contains the opposite side. ◦ Every triangle has three altitudes.

31.  A median is a segment that connects the vertex of a triangle to the midpoint of the opposite side. ◦ Every triangle has three medians.  A midline is a segment that connects the midpoints of two sides of a triangle. ◦ Every triangle has three midlines.

32.  Do each of the following constructions, and write down how you did it.  You may not use rules, protractors, or other measuring tools. 1) Draw a line. Then construct a line perpendicular to the first line. 2) Draw a line. Then construct a line parallel to the first line. 3) Draw an angle. Then construct its bisector.

33.  Read Section 7.06 (pages 577-581)  Page 582 #10-16  Page 584 #1-8 (Investigation 7B Reflection)

36.  Do each of the following constructions with your partner, and write down how you did it.  You may not use rulers, protractors, or other measuring tools. 1) Draw a line. Then construct a line perpendicular to the first line. 2) Draw a line. Then construct a line parallel to the first line. 3) Draw an angle. Then construct its bisector.

37. 1) Draw a line. Then construct a line perpendicular to the first line. 2) Draw a line. Then construct a line parallel to the first line. 3) Draw an angle. Then construct its bisector.

38.  An altitude is a perpendicular segment from a vertex of a triangle to the line that contains the opposite side. ◦ Every triangle has three altitudes.

39.  A median is a segment that connects the vertex of a triangle to the midpoint of the opposite side. ◦ Every triangle has three medians.  A midline is a segment that connects the midpoints of two sides of a triangle. ◦ Every triangle has three midlines.

41.  Netbooks  Needs to be installed

43.  Read Section 7.06 (pages 577-581)  Page 582 #10-16  Page 584 #1-8 (Investigation 7B Reflection)