Help with a Logical Deduction Q from Holt Geometry

[Pamela in VA]

Given: If m<ABC = m<CBD, then

__›

BC bisects <ABD.

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BC bisects m<ABD.

Conjecture: m<ABC = m<CBD.

WHY is this conjecture invalid using the Law of Detachment? That's what the answer key says, but it doesn't make sense to me.

(Holt 2007 Geometry 2-3 Practice B worksheet #3)

THANKS!

Pamela F. in VA

[Jann in TX]

First of all the Law of Detachment is valid if both p and q are valid (hypothesis and conclusion).

 

In problem 3 the statement is:

If the measure of angle ABC = the measure of angle CBD then ray BC bisects angle ABD. No figure is given.

 

It goes on to tell you that Ray BC does in fact bisect angle ABD.

 

The conjecture is that the measure of angle ABC = the measure of angle CBD. It does not tell you this is true-- and you can easily draw a counter example showing otherwise...

 

So while the conclusion is true-- the hypothesis has not been proven to be true-- so the conjecture is invalid.

 

--

I skimmed most of this chapter with my class-- it is VERY difficult to cram a semester of formal logic into one small chapter of Geometry. I covered the basics. E-mail me if you want to see the test I used for this chapter.

 

I rather spend more time on proofs and formula work...

 

Jann

[Pamela in VA]

Thanks Jann! I guess I was assuming the angles were part of the same figure, but since no figure was given that does not necessarily follow. The rest of your explanation now makes sense.

 

I would love to see the test you used for this Chapter. We will be studying formal logic next semester, so we may come back to these exercises in more depth then.

 

As always, your expertise in this area is greatly appreciated!

Pamela F. in VA

freeman4him@gmail.com