Two Column Proof Week
Friday, November 15, 2013
10:53 AM
Slide
Notes
Two column proofs will be the topic all through the week this
week and the entire week's worth of definitions, theorems,
postulates, and properties you are to memorize are found in
the "Reasons" section of this lesson.
Let's look at how two column proofs are set up. You will be
presented with a given statement which will always be what
you start out with in your two column proof.
Often, you will also be given a figure to base your statements
and reasons on.
You will take what you learn about definitions, theorems,
postulates, and properties to get to the end point that the
problem specifies. At the end, often people put Q.E.D. showing
that they feel they have proven the geometric point of the two
column proof.
Let's try an example.
You are given that line AB is congruent to AD and that line BC is
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You are given that line AB is congruent to AD and that line BC is
congruent to CD. Prove that a line AC would be perpendicular
bisector of line BD.
First, we need to create the line that goes from A to C so that
we actually get a line that bisects BD. That can be done using
the reason of the reflexive property. That basically means that
the line is equal to itself.
Now we can work with triangles so that we can show BD
getting split in the middle by AC. Triangle ABC is congruent to
triangle ADC using side side side which you learned about in an
earlier lesson.
Now you can use the Corresponding sides of congruent
triangles are congruent to show that angle ABC is congruent to
ADC.
What we really need though is to get triangles that have a sides
on the line BD next. We will add a point E to help with that. To
get that point in there we will use the reflexive property much
as we did to get the line AC earlier.
Now we will follow steps very much like we did in the earlier
statements but this time working with the smaller triangles. We
will use SSS and CPCTC again.
Now we have two equal segments.
CPCTC will get us to the point of getting two of the angles and
now we merely need to show we have right angles to get the
perpendicular part.
QED
In the section of this lesson called Reasons, you will come back
each lesson day this week to memorize the reason statements
that are commonly used in addition to the ones shown here in
this example.
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