Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1226.
Per van Aubel's theorem, Lines O1O3 and O2O4 are equal length and cross at right angleWe have M1M2=1/2. O1O3=M3M4 and M1M2//O1O2//M3M4and M1M4= 1/2. O2O4=M2M3 and M1M4//O2O4//M2M3so M1M2M3M4 is a square
That M1M2M3M4 is a parallelogram is easily seen from the midpoint theorem To show that this parallelogram is indeed a square we need to show that O1O3 and O2O4 are equal and cut at right angles - this follows easily from Van Aubel's theorem.