Question

How do you do two-column geometrical proofs?

Answer 1

Draw a table with two columns;
in the first column write things you know ("Statements" or "Assertions");
in the second column write the Reason you know the corresponding assertion is true.

Explanation:

This is perhaps best explained with an example:
If a line `AB` intersects another line `CD` at a point `M`
prove that `/_AMD = /_CMB`

#{: (color(black)("Assertion")," | ",color(black)("Reason")), (bar(color(white)("XXXXXXXXXXXXXXXXXX"))," | ",bar(color(white)("XXXXXXXXXXXX"))), (/_AMD+/_DMB = 180^@," | ","Definition of a straight line"), (bar(color(white)("XXXXXXXXXXXXXXXXXX"))," | ",bar(color(white)("XXXXXXXXXXXX"))), (/_CMB+/_DMB = 180^@," | ","Definition of a straight line"), (bar(color(white)("XXXXXXXXXXXXXXXXXX"))," | ",bar(color(white)("XXXXXXXXXXXX"))), (/_AMD+/_DMB = /_CMB+/_DMB," | ","Thing that are equal to the same"), (," | "," thing are equal to each other"), (bar(color(white)("XXXXXXXXXXXXXXXXXX"))," | ",bar(color(white)("XXXXXXXXXXXX"))), (/_AMD = /_CMB," | ","Subtracting the same amount from"), (," | "," both sides of an equality leaves an equality"), (bar(color(white)("XXXXXXXXXXXXXXXXXX")),,bar(color(white)("XXXXXXXXXXXX"))) :}#