iven: ΔMNO Prove: The medians of ΔMNO are concurrent. Given triangle of sides M (x1, y1), N (x2, y2) and O (x3, y3) point to the same triangle on the graph of x-axis and y-axis, with M prime (0, 0), O prime (2t, 0) and N prime (2r, 2s) has a midpoint s formed by connecting Prime PQR Proof: Statements Reasons 1. ∆MNO Given 2. Use rigid transformations to transform ΔMNO to the congruent ΔM'N'O' so that M' is at the origin and M'O' lies on the x-axis in the positive direction. Rigid transformations result in congruent shapes. 3. Any property that is true for ΔM'N'O' will also be true for ΔMNO. Definition of congruence 4. Let r, s, and t be real numbers such that the vertices of ΔM'N'O' are M'(0,0), N'(2r,2s), and O'(2t,0). Defining constants 5. Let P', Q', and R' be the midpoints of M'N', N'O', and M'O', respectively. Defining points 6. P' = (r,s); Q' = (r + t,s); R' = (t,0) ? 7. Definition of slope 8. Applying point-slope formula 9. and intersect at point S. Algebra 10. Point S lie