1. Geometry -20 + |-35|, October 2012 HEAD UPS- new seats! HEAD UPS- new seats! 1)Warm up: (top front) a) Briefly define/ sketch a) Briefly define/ sketch perpendicular bisector perpendicular bisector b) Draw then duplicate, using construction tools: b) Draw then duplicate, using construction tools: i) TWO segments i) TWO segments ii) one acute angle iii) one obtuse angle

2. Objective Students will be able to construct perpendicular lines and practice with construction tools.

3. homework DUE TUESDAY: Definitions (word, define, sketch in vocab section): Definitions (word, define, sketch in vocab section): sketch, draw, construct, perpendicular bisector, angle bisector, altitude, median, midsegment (triangle), circumcenter, centroid 3.1, pg. 147: 1 – 10 (need patty paper) 3.1, pg. 147: 1 – 10 (need patty paper) Write a paragraph- what are geometric constructions? when were they first used and why do we study them today? [document your source] possible source: http://www.mathopenref.com/constructions.html Write a paragraph- what are geometric constructions? when were they first used and why do we study them today? [document your source] possible source: http://www.mathopenref.com/constructions.html

4. important distinctions sketch– quickly by hand draw- use tools (protractor and ruler) (protractor and ruler)construct- ONLY use a compass and straightedge http://www.mathopenref.com/constructions.html

5. when you construct an arc…. what is the distance called from the point of your compass to your arc?

6. Constructing Perpendiculars Perpendicular bisector: a line or segment that bisects a segment and is also perpendicular to the segment bisector – divide into two congruent parts

7. Use patty paper 1) Draw a line segment Mark and label the endpoints A and B 2) Find the perpendicular bisector. with patty paper HOW DO YOU THINK YOU CAN find the line that is perpendicular to line segment AB and also through the midpoint with patty paper? something Hint: Try something!

8. 3.2, pg. 149 read together Constructing Perpendicular Bisectors Investigation 1: with patty paper How would you describe the relationship of the points on the perpendicular bisector to the endpoints of the bisected segment? DISCUSS Step 4– whole group! Perpendicular Bisector Conjecture: on the perpendicular bisector If a point is on the perpendicular bisector of a segment, then it is EQUIDISTANT from the endpoints

9. perpendicular bisector http://www.youtube.com/watch?v=5bvjnleMn5A http://www.mathopenref.com/constbisectline.html http://www.youtube.com/watch?v=d62zCNZP0wg&feature=related http://www.youtube.com/watch?v=09aYOtI7v2g&feature=related Investigation 2: with a compass and straightedge Draw 5 line segments Construct the perpendicular bisector for each. Converse of the Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, it is on the perpendicular bisector then it is on the perpendicular bisector of the segment.

10. do you know these words? 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

11. exit quiz- on quarter sheet 1) Draw a line segment and label it AB. Duplicate your segment. 2) Construct the perpendicular bisector for one of your segments (original or duplicated) 3) Draw an angle. Duplicate it using your construction tools.