1. Geometry October 2012 1)Place binder and text on desk. 2)WARM UP (top front) Squares on a side 123456...35...n Shaded squares013610__...___...____ Below is a pattern of square arrays. How many shaded squares are in an array with 6 squares on a side? With 35 squares on a side? With n squares on a side?

2. Objective Students will be able to apply the basic six constructions to construct medians and altitudes. DUE TUESDAY Complete Constructions Study Guide Complete Constructions Study Guide Wednesday- October 24 Chapter 3/ Rule Writing Test Chapter 3/ Rule Writing Test OPTIONAL HW- Quiz Corrections due OPTIONAL HW- Quiz Corrections due FALL BREAK October 25 and 26 PROJECT- Shuttling Around due October 30

3. Constructions Quiz OPTIONAL Homework Assignment Quiz Corrections On a separate paper: 1) Write the problem 2) State what you did incorrectly 3) Re-work the problem correctly ATTACH to your original quiz DUE by October 24th

4. angle vocabulary review By sides: scalene- no congruent sides isosceles- at least 2 congruent sides equilateral- 3 congruent sides By angles: right- one 90⁰ angle acute- all angles less than 90⁰ obtuse- one angle greater than 90⁰ http://www.youtube.com/watch?v=DUNxLGhFCqM

5. median segment connecting the vertex of of a triangle to the midpoint of the opposite side each triangle has 3 medians midsegment segment connecting midpoints of two sides of a triangle each triangle has 3 midsegments do you know these words?

6. median the segment connecting the vertex of a triangle to the midpoint of its opposite side median

7. midsegment the segment that connects the midpoints of two sides of a triangle midsegment

8. and…. circumcenter- the point of concurrency (one point where all 3 lines intersect) for the perpendicular bisectors.

9. altitude- perpendicular segment from a vertex to the opposite side or a line containing the opposite side http://www.mathwarehouse.com/dictionary/A-words/altitutude.html

10. altitude the perpendicular segment from a vertex to the opposite side or a line containing the opposite side

11. Term Definition Examples Shortest distance conjecture The shortest distance from a point to a line is measured along the perpendicular segment from the point to the line. angle bisector conjecture If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. altitude The altitude of a triangle is a perpendicular segment from a vertex to the opposite side or a line containing the opposite side. median A line segment connecting a vertex of a triangle to the midpoint of the opposite side midsegment A segment connecting two midpoints of two sides of a triangle Chapter 3- add to conjectures section

12. Basic SIX Constructions (practice until you master) 1) Duplicate line segment 2) Duplicate angle 3) Construct perpendicular bisector 4) Construct perpendicular from a pt. not on line 5) Construct angle bisector 6) Construct parallel lines (see book- page 164) http://www.youtube.com/watch%3Fv%3DVvSLFMdDEZs

13. More Constructions With patty paper: 1) medians 2) altitudes 3) midsegments With compass and straightedge: 1) medians 2) altitudes 3) midsegments

14. Patterns? Draw FOUR large triangles on your paper. Different group members try different triangles Different group members try different triangles acute, obtuse, right, scalene, isosceles acute, obtuse, right, scalene, isosceles 1) Construct all 3 perpendicular bisectors for one. 2) Construct all 3 medians for one. 3) Construct all 3 midsegments for one. 4) Construct all 3 altitudes for one. What do you notice about where these lines intersect? Check the distance from any intersection points to each vertex? Are there any patterns? What about your group mates?

15. Debrief Which constructions do you need to practice so that you have mastered them? what is the difference between a sketch and a construction?