2003 Indonesia MO Problems/Problem 2
Revision as of 00:26, 11 August 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 2 -- good ol' IM2 days)
Problem
Given a quadrilateral . Let
,
,
, and
are the midpoints of
,
,
, and
, respectively.
and
intersects at
. Prove that
and
.
Solution
Draw lines and
. By SAS Similarity,
and
That means
and
making
a parallelogram.
Since is a parallelogram,
In addition, by the Alternating Interior Angle Theorem,
and
Thus, by ASA Congruency,
Finally, using CPCTC shows that
and
See Also
2003 Indonesia MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 3 |
All Indonesia MO Problems and Solutions |