1. AMNO Given
2. Use rigid transformations to transform AMNO to the congruent AM'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.
Definition of
congruence
3. Any property that is true for AM'N'O' will also be true for AMNO.
Defining constants
Defining points
?
4. Let r, s, and t be real numbers such that the vertices of AM'N'O' are M(0,0), N(2r,2s), and
0 (21,0).
5. Let P', Q', and R' be the midpoints of M'N', N'O', and M'O', respectively.
6. P' = (r, s); Q' = (r + t, s); R' = (t,0)
7.
slope of M'Q = $t; slope of N'R' = 2729 ; slope of O'P' = 25
A
MO
2725.75 22517; O'P' = 22 +2.254,
8.
mo 'and NR'intersect at point:
s(+36 + 1)-33).
=
Definition of slope
*; NR
Applying point-slope
formula
Algebra
9.
The coordinates of S
satisfy the equation of
OP
10. Point S lies on of
11. All three lines share point S.
Follows from 9 and 10
Definition of concurrent
lines
12. The medians are concurrent.
of for step 6?