C HAPTER 5

C HAPTER 5 G LOSSARY T ERMS Define the following and put in your glossary Perpendicular bisector Median Altitude Indirect Proof Concurrent Lines Circumcenter Centroid Orthocenter Incenter Prepare for Constructions!

I F YOU FORGET YOUR MATERIALS.. 1. You are “responsible” for having paper, pencil and book in class everyday. 2. If you forget, first ask another student if you may borrow... Pencil, paper, book.. 3. If you must borrow from me you have two choices. Borrow from Teacher, requires completion of 5 extra homework problems and collateral. (Phone, wallet) Purchase 1 pencil for a quarter. Lead Pencil $.50 Payment due immediately. Students with no warnings receive 2 points on overall grade. Borrowed pencils/books must be returned in same condition as received. Mrs. Motlow Classroom Procedures

C ONSTRUCTIONS Bisector of a side of a triangle Median of a Triangle Altitude of a Triangle Angle Bisector of a Triangle Please take good notes as you will be expected to replicate on your own.

C ONSTRUCT THE BISECTOR OF A SIDE OF A TRIANGLE Adjust compass to ½ AC. Place the compass at vertex A and draw an arch above and below AC. Using the same compass settings place the compass at vertex C. Draw and arc above and below AC. Label the points of the intersection of the arcs P and Q. Use a straight edge to draw PQ. Label the point where PQ bisects AC as M. Note that this is a perpendicular bisector. Construct bisectors for AB and AC What do you notice about the three bisectors? This point is called the circumcenter B AC P Q M

C ONSTRUCT A MEDIAN OF A TRIANGLE Adjust compass to ½ AC. Place the compass at vertex B and draw an arch above and below BC. Using the same compass settings place the compass at vertex C. Draw and arc above and below AC. Label the points of the intersection of the arcs R and S. Label point where RS crosses BC as M. AM is a median of  ABC Construct medians for the other two sides. What do you notice about the three medians? This point is called the centroid B AC S R M

C ONSTRUCT AN ALTITUDE OF A TRIANGLE Place the compass at vertex B and draw two arcs intersecting AC. Label the points where the arcs intersect the side X and Y. Adjust the compass to an opening greater than ½ XY. Place the compass on X and draw and arc above AC. Using the same setting place the compass on Y and draw an arc above AC. Label the intersection of the arcs H. Use a straightedge to draw BH. Label the point where BH intersects AC as D. BD is an altitude of ABC and is perpendicular to AC. Construct Altitudes to the other two sides. What do you notice about the three altitudes? This point is called the orthocenter. B AC XY H

C ONSTRUCT AN ANGLE BISECTOR OF A TRIANGLE Place the compass at vertex A and draw arcs through AB and AC. Label the points where the arcs intersect the sides as J and K. Place the compass on J and draw and arc. Then place the compass on K and draw an arc intersecting the first arc. Label the intersection L. Use a straightedge to draw AL. AL is the angle bisector of  ABC Construct angle bisectors for the other two angles. What do you notice about the three bisectors? This point is called the In Center B AC J K L

P RACTICE A SSIGNMENT Complete the four constructions (Bisectors, medians, altitudes, angle bisectors) for the four different triangles. Make conjectures for questions at the bottom of the page.

A B C 3 A B C 1 A B C 2 A B C 4

9c. A B C c. A B C a. A B C b. A B C d. 1.Where do the lines intersect for acute, obtuse and right triangles? 2. Under what circumstances do the special lines of a triangle coincide with each other?