University:
High School
Course:
High School Geometry
Academic year:

2023
Views:

289

Pages:

3
Author:

noulleync26

Medians & Altitudes of Triangles In your own words, write the meaning of each vocabulary term. median of a triangle: a segment that bisects a side and goes to the opposite corner altitude of a triangle: a segment that is perpendicular to a side from the angle Theorems Theorem 6.7 Centroid Theorem The centroid of a triangle is two-thirds of the distance from each vertex to the midpoint of the opposite side. The medians of 1 ∆ABC meet at point P, and 1. AP = (2/3)AE, BP = (2/3)BF, and CP = (2/3)CD Orthocenter The lines containing the altitudes of a triangle are concurrent, and the point of concurrency is the orthocenter of the triangle. The lines containing AF, BD, and CE meet at the orthocenter G of ∆ABC Extra Practice In Exercises 1-3, point P is the centroid of ΔLMN. Find NP and QP. QN = 33 NP = 2/3 * QN NP = 2/3 * (33) NP = 22 QP = 11 QN = 45 NP = 2/3 * QN NP = 2/3 * (45) NP = 30 QP = 15 QN = 39 NP = 2/3 * QN NP = 2/3 * (39) NP = 26 QP = 13 In Exercises 4 and 5, point D is the centroid of ΔABC. Find CD and CE. DE = 7 CD = 2/3 * CE 7 = 1/3 * CE 21 = CE CD = 2/3 * 21 CD = 14 DE = 12 CD = 2/3 * CE 12 = 1/3 * CE 36 = CE CD = 2/3 * 36 CD = 24