Warm Up Homework – page 7 in packet Complete the “Location, Location, Location” worksheet. You will need to place points at each Store location in order to find where the distribution center should be built. You may use your notes, but not your neighbor to solve the problem.

22. Proof of the Angle Bisector Theorem 2. DE, equidistant Ray BD bisects angle ABC, so D is equidistant from the sides of angle ABC Trans. Property of = Bisector D is equidistant from the sdies of Triangle ABC, steps 2-4

Chapter 5.3 Medians and Altitudes of a Triangle Students will identify and construct the median, the altitude, and the perpendicular bisector of the sides of a triangle.

Vocabulary median of triangle- a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. centroid of the triangle- the point of concurrency of the three medians.

Finding the Balancing Point Using the index card and straightedge provided, draw and cut out a triangle. (Make sure each group member’s triangle is different.) Fold each side in half to find the midpoint. Connect each midpoint to the opposite vertex. Place a point and label it P at the point of concurrency. Balance the tip of a pencil at the centroid

Theorem 5.7 Concurrency of Medians of a Triangle The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

Warm Up: Day 2 Segment CD is the median for Triangle ABC. Solve for x.

Concurrency of Medians of a Triangle The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. If P is the centroid of ABC, then AP = 2/3AD, BP = 2/3BF, and CP = 2/3CE B C A

Construction of a Perpendicular Bisector from a point to a line.

More Vocabulary altitude of a triangle- the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side. An altitude can lie ______________ the triangle. orthocenter of the triangle- the point of intersection of the altitudes. inside, outside, or on

Where does the orthocenter occur? acute right obtuse

Concurrency of Altitudes of a Triangle The lines containing the altitudes of a triangle are concurrent. If AE, BF, and CD are the altitudes of ABC, then the lines AE, BF, and CD intersect at some point H. B C A

Construct the Orthocenter for triangle ABC.

Find the coordinate of the centroid of triangle JKL.

Warm Up Turn to the construction warm up in your packet!

Sometimes, Always, Never

Get out your charts!!!