TEAM PROJECT. Geometric Applications. To increase your

Chapter 9, Problem 9.1

(choose chapter or problem)

TEAM PROJECT. Geometric Applications. To increase your skill in dealing with vectors, use vectors to prove the following (see the figures). (a) The diagonals of a parallelogram bisect each other. (b) The line through the midpoints of adjacent sides of a parallelogram bisects one of the diagonals in the ratio I: 3. (e) Obtain (b) from (a). (d) The three medians of a triangle (the segments from a vertex to the midpoint of the opposite side) meet at a single point, which divides the medians in the ratio 2:1. (e) The quadrilateral whose vertices are the midpoints of the sides of an arbitrary quadrilateral is a parallelogram. (n The four space diagonals of a parallelepiped meet and bisect each other. (g) The sum of the vectors drawn from the center of a regular polygon to its vertices is the zero vector. ~ w a Team Project 38(a) o~ a c C _ b ~ D~B A a Team Project 38{d) Team Project 38(e)