5-3: Medians and Altitudes of Triangles Page 311 12) 59.7 13) 63.9 14) 62.8 15) 16) (-2.5, 7) 17) (-1.5, 9.5) 18) 8.37 19) 55° 22) Angle Bisector, mBAE = mEAC 23) Perpendicular Bisector, mBAE = mEAC 24) Angle Bisector, mABG = mGBC 25) Neither, no indiciation where Angle C is a bisector 26) Neither 27) 28) Never 29) Sometimes 30) 31) 32) 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

Medians and Altitudes of Triangles Section 5-3 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Definitions Centroid is the balancing point or center of gravity of the triangle using the midpoint of each side and the vertex of the 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. The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side Orthocenter are the three altitudes of a triangle Altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side; the height of the triangle is the length of the altitude 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Identify Centroid Centroid is the balancing point or center of gravity of the triangle using the midpoint of each side and the vertex of the triangle. 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Identify Centroid Centroid is the balancing point or center of gravity of the triangle using the midpoint of each side and the vertex of the triangle. 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Video of Centroid http://www.youtube.com/watch?v=nSYxJ6opZhs 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 1 In ∆LMN, RL = 21 and SQ = 4. Find LS. 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 2 In ∆LMN, RL = 21 and SQ = 4. Find RS + NQ. 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Your Turn In ∆JKL, ZW = 7, and LX = 8.1. Find KW. 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 3 A sculptor is shaping a triangular piece of iron that will balance on the point of a cone. At what coordinates will the triangular region balance? 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

Steps in finding the Orthocenter Graph the triangle Write an equation from the altitude to a vertex Write another equation from the altitude to the vertex Create a system to determine the orthocenter 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Identify Orthocenter Orthocenter are the three altitudes of a triangle; Prefix: STRAIGHT 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Altogether… 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Identify Orthocenter Orthocenter are the three altitudes of a triangle; Prefix: STRAIGHT orthocenter 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 4 Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1). 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 4 Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1). 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 4 Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1). 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Example 5 Find the orthocenter of ∆KLM with vertices K(2, –2), L(4, 6), and M(8, –2). 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Your Turn Find the orthocenter of ∆PQR with vertices P(–5, 8), Q(4, 5), and R(–2, 5). 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles

5-3: Medians and Altitudes of Triangles Assignment Pg 317 12-15, 17-31 odd, 34-37 all Quiz BLOCK DAY 12/1/2018 7:15 AM 5-3: Medians and Altitudes of Triangles