http://www.ck12.org Chapter 2. Reasoning and Proof
Example A
Write a two-column proof for the following:
IfA,B,C, andDare points on a line, in the given order, andAB=CD, thenAC=BD.
First of all, when the statement is given in this way, the “if” part is the given and the “then” part is what we are trying
to prove.
Always start with drawing a picture of what you are given.
Plot the points in the orderA,B,C,Don a line.
Add the corresponding markings,AB=CD, to the line.
Draw the two-column proof and start with the given information.From there, we can use deductive reasoning
to reach the next statement and what we want to prove.Reasons will be definitions, postulates, properties and
previously proven theorems.
TABLE2.19:
Statement Reason
1.A,B,C, andDare collinear, in that order. 1. Given
2.AB=CD 2. Given
3.BC=BC 3. Reflexive PoE
4.AB+BC=BC+CD 4. Addition PoE
5.AB+BC=AC,BC+CD=BD 5. Segment Addition Postulate
6.AC=BD 6. Substitution or Transitive PoEWhen you reach what it is that you wanted to prove, you are done.
Example B
Write a two-column proof.