Show that the green dotted line, which is an altitude of the blue triangle, is also a median of the orange triangle.

Solution

The conclusion about a median of the orange triangle holds for any cevian of the original blue triangle – It need not be an altitude.

See also The owl of Ceva for the first step.

Show that the green dotted line, which is an altitude of the blue triangle, is also a median of the orange triangle. https://t.co/UM8NOTdWBy By @MarshallWBuck pic.twitter.com/wZYYaWO62M

— Mirangu (@Mirangu1) December 22, 2023