1. 3.7—Medians and Altitudes of a Triangle Warm Up 1. What is the name of the point where the angle bisectors of a triangle intersect? Find the midpoint of the segment with the given endpoints. 2. (–1, 6) and (3, 0) 3. Write an equation of the line containing the points (3, 1) and (2, 10) in point-slope form.

2. 3.7—Medians and Altitudes of a Triangle Objective: Use properties of ______________ and ___________ of a triangle. Median of a triangle: a segment whose ____________ are a ________ of a triangle and the midpoint of the ____________ side Centroid of a triangle: the point of ______________ of the _____________ of a triangle mediansaltitudes endpointsvertex opposite concurrency medians The centroid is __________ inside the triangle. (The centroid is also the balancing point of a triangle.) always

6. ___________ of a triangle:the _____________ segment from a _________ to the __________ side (or to the _________ that contains the opposite side) ________________ of a triangle: the point of ____________ of the altitudes of a triangle Altitude perpendicular vertex opposite line Orthocenter concurrency

8. Examples: 3.Given the coordinates of the vertices of ΔXYZ are X(9, –5) Y(–2, 3) Z(4, –6) a.Find the equation of the line containing the side b. Find the equation of the line containing the altitude from X to.

10. Construct the Centroid of the triangle.

11. Construct the altitude from each vertex to the opposite side using the perpendicular from a point to a line construction.

12. Construct the Orthocenter of the triangle.