1. Constructing Perpendicular Bisectors and Lines Right angles Cut in Half

2. Terms Bisector – To cut in half, divided into 2 congruent segments or parts Perpendicular – When they intersect they form right angles

3. Constructing a perpendicular Bisector Investigation pg 150

4. Con’t

5. Process 1.Place pointy end of compass and extend pencil end so it is more than halfway across segment, swing an arc above and below the segment 2.With same compass setting swing arc from second endpoint so it crosses the first arc both above and below the segment 3.Connect the intersections of the two arcs I call this making a piece of candy, because that is what it looks like

6. Other Process What if you can’t swing an arc above or below the segment 1.Place pointy end on one endpoint and swing an arc that is greater than half the segment 2.Do same arc from other endpoint 3.Repeat step 1 and 2 with a different arc 4.Connect the two intersections

7. Conjectures Perpendicular Bisector Conjecture If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints Convers of Perpendicular Bisector Conjecture If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

8. Median of a Triangle Median is a segment that connects the vertex of a triangle to the midpoint of the side opposite How would I construct this? Find the midpoint, How? Perpendicular bisector Connect the vertex and midpoint

9. Midsegment of a Triangle Midsegment of a Triangle is a segment that connects two midpoints. How would you construct a midsegment? Find the midpoint of two sides Connect midpoints with a segment

10. Example 1.Draw a triangle and label it ABC 2.From point a construct a median 3.From sides AB and AC construct a Midsegment

11. Perpendicular Lines Investigation pg 154

12. Continues

13. Perpendicular Lines Constructing a Line perpendicular to another line through a specific point. 1.Place pointy end on point not on the line 2.Swing an arc the will intersect the line in two places 3.Place point end on one intersection and swing arc on other side of line (do not change the size of the comp 4.Repeat with other intersection point 5.Connect original point with the intersection of the arcs

14. Shortest Distance Conjecture The shortest distance from a point to a line is measured along the perpendicular segment for the point to the line

15. Altitude The altitude or height of a triangle is a segment from a vertex perpendicular to the side opposite, this doesn’t necessarily bisect the side or angle

16. Examples Pg 151 2,3 Pg 156 5

17. Homework Pg 1511,4,5,7,8,9 Pg 1561-4