Homework Quiz
Warmup
Need Graph Paper/Compass
5.3 Concurrent Lines, Medians, and Altitudes
Learning Target I can tell the difference between a median, altitude, perpendicular bisector and angle bisector of a triangle.
When three or more lines intersect at one point, they are concurrent. The point at which they intersect is called the point of concurrency.
Circumcenter of a Triangle: The point of concurrency of the perpendicular bisectors of a triangle. The points of a triangle are equidistant from the circumcenter The circumcenter of a triangle is also the center of the circle circumscribed about the triangle.
Lets Practice Please write the following problems down
Do #1-3
Do #11-13 Find the circumcenter only
Incenter of a Triangle: The point of concurrency of the angle bisectors of a triangle. Here the circle is inscribed in the triangle
Name the point which represents the incenter
Median of a Triangle: A segment whose endpoints are a vertex and the midpoint of the opposite side. EX
Centroid: the point of concurrency of the medians. Note…its also called the center of gravity of a triangle because it is the point where the triangle will balance.
Something to know… The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. EX:
Altitude of a triangle: the perpendicular segment from a vertex to the line containing the opposite side.
In an acute triangle, the altitude is inside the triangle. In a Right triangle the altitude is a side. In an obtuse triangle, an altitude will be outside of the triangle.
Orthocenter of a Triangle: Point of concurrency for altitudes of a triangle.
Lets do on the worksheet
Constructions -Incenter -Circumcenter
RECAP ( A lot to keep track of here): Perpendicular Bisectors Circumcenter Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter
On the worksheet, do #5-10
Review 5.1 p.246 #2-18 even, #22-25, #29-31 (tougher)
Review 5.2: p.251 #1-25 (skip 5, 11, 16, 17)
Review 5.3 p #2-22, 27-28
QUIZ Tomorrow on