Bill F. answered • 01/09/13

Experienced Teacher & Tutor in Round Rock, TX

Short answer: carefully! Just use what you know to "prove" any statement you write.

The whole idea of using the two columns is to help you think of each step to use when "proving" why something is true (or not).

As a simple example: if we draw two intersecting lines, like a large X, we form 4 angles around the intersection (where the lines meet). If we name the top angle in our "X" as angle a, and the bottom angle (opposite the top-angle) as angle b, then we can make a statement in our left "Statements" column that "angle a = angle b".

But how do we know that, and how do we prove it? We use the right "Reasons" column to answer that: in this example, we'd write "Vertical angles are congruent", which is a basic geometry definition.

This same reasoning applies to more complex geometry statements, as in triangle identities which prove that two triangles are identical (congruent) in all 3 sides and angles, based on side-angle-side (SAS) or side-side-side (SSS). If you observe that all three sides of "triangle ABC" have identical lengths with matching sides another "triangle DEF", then you can state that both triangles are congruent in the left "statements" column, based on the right-column "Reason" of SSS. Make sense now?