I do not understand how to do flow/two column/paragraph proofs in geometry.

Question

For example, we are expected to prove that two lines or angles are congruent by postulates. We are also supposed to write a congruence statement AND the parts that make it congruent (3 minimum). Although I understand this to an extent, I don't understand the differences between the congruence statement reasons, such as Side angle side (SAS), Side side side (SSS), angle angle angle (AAA), HL and how I will know when to use them. 

Answer 1

Personally, I think that you ned to study your textbook and/or lecture notes more, and TO ASK QUESTIONS DURING GEOMETRY CLASS--that's what the teacher is there for!

 

Here is a little narrative on triangle congruence methods.  For example, consider SAS.  That means that two triangles will be shown to be congruent by virtue of three statements. Consider triangles ABC and DEF.

 

If AB = DE by reason of these sides being equal in length(a.k.a. congruence), that one pair of corresponding sides.

If BC = EF by virtue of their given equality, that's a second pair of corresponding sides.

 

Note that the vertex angle B is formed by sides AB& BC in one triangle, and

vertex angle E is formed by sides DE & EF in the other triangle.

 

If, then, we also know that angles B and E have identical measures (are equal, which is the same as congruence), then we have the "A" part of "SAS" as proof of triangle congruence; angles A and E are the INCLUDED angles.

 

Once you realize that drawing triangle ABC as side AB, then an angle at B and finally a second side BC, then you have fully determined a unique triangle (connect A to C).  Drawing triangle DEF will REPLICATE the same (congruent) triangle because of the SAS equalities of DE, angle E and EF.  

 

Sketch this out and study it...until you fully understand why these triangles are congruent in the SAS case.