proof with extra step

Question

I have a test tomorrow and I still don't know how to write a proof. I know the basis (first step is given) but from there its basically Portuguese to me ! I know CPCTC but I don't know the steps in between! please help! I also know - SAS/ASA/AAS/SAA/HY-LEG

Answer 1

Hi Ariel,

You didn't ask for a particular proof to be shown.

My suggestion is to carefully look over each proof shown in the intro/directions for each section of the chapter.  Strive to understand them - how they started, how they progressed to the 'prove' statement and what was the reason stated for each step.  Maximize the use of the textbook.

You are correct to say the first step can be the 'given' information.  Carefully look at the 'given' information and see if there are any conclusions you can draw from it/them.  See if that conclusion can lead you toward the 'prove' statement.  If there is a drawing for each proof, notice what you can conclude by looking at the drawing, such as one of the segments being in each triangle, so you can declare that segment congruent to itself (Reflexive Property) and that may help you conclude if the triangles are congruent by SSS, SAS, ASA or AAS.  Is there a segment that has been bisected (a 'given' statement)?  That would allow you to conclude that the two portions of the original segment are congruent to each other (Definition of a segment bisector) and would help you to conclude another set of segments are congruent, meaning the remaining possible methods to prove the triangles are congruent are SSS and SAS.   Good luck, Ariel.

Mary Ann