Lesson 3.7 & 3.8: 1.Homework Collection 2.Constructions

Warm Up: Make sure you have the following items at your desk: 1.Paper 2.Pencil 3.Compass 4.Straightedge Complete the Warm Up handout and add it to your notes.

Point of Concurrency: A point of concurrency is a point of intersection for 3 or more lines. Concurrent lines Not concurrent lines

Activity #1: Angle Bisector Concurrency – do you think the angle bisectors of a triangle will be concurrent? Using the Handout (#1), a compass, and a straightedge, construct the angle bisectors of triangle ABC.

Summary: Add this to your Learning Targets Packet. The three angle bisectors of a triangle ______________________________. They meet at a point called the ______________.

Activity #2: Perpendicular Bisector Concurrency – do you think the 3 perpendicular bisectors of a triangle will be concurrent? Using the Handout (#2), a compass, and a straightedge, construct the perpendicular bisectors of each side of each triangle.

Summary: Add this to your Learning Targets Packet. The three perpendicular bisectors of a triangle _____________________________. They meet at a point called the _______________.

Activity #3: Altitude Concurrency – do you think the 3 altitudes of a triangle will be concurrent? Using the Handout (#3), a compass, and a straightedge, construct the altitudes of each side of each triangle. (Construct a perpendicular from a point off the line.)

Summary: Add this to your Learning Targets Packet. The three altitudes (or the lines containing the altitudes) of a triangle ___________________. They meet at a point called the ______________________.

Activity #4: Median Concurrency – do you think the 3 medians of a triangle will be concurrent? Using the Handout (#4), a compass, and a straightedge, construct the medians of each side of each triangle. (Find the midpoint of each side by finding the perpendicular bisector and then connect the midpoint to the opposite angle.)

Summary: Add this to your Learning Targets Packet. The three medians of a triangle ___________________________. They meet at a point called the ______________________. Look at p. 186 – we will do this together.

Thoughts: For what kind of triangle will the incenter, circumcenter, and orthocenter be at the same point? What about the cen What about the centroid??

Homework: P : 8, 12 P : 1-18 all