Last Set of Tips - Multiplication and Division Properties

Using the Multiplication and Division Properties in Proofs

1.  Look for a double use of the word midpoint or trisect or bisect in the Givens.

2.  Use the Multiplication property when the segments or angles in the Prove are larger than those in the Given.

3.  Use the Division property when the segments or angles in the Prove are smaller than those in the Given.

(taken from Geometry for Enjoyment and Challenge, McDougal & Littell, Evanston, 1991, p.90)

Read and reread the above steps, until you understand them!!

Tips:
#1, 3, 4, 5)  Two-step proofs.

#6)  Two-stepper but be careful.

#8)Why is this in there?!  Two steps, ridiculously easy!!

#11)  Fun proof!  Ignore the first given for a moment.  Use the other three with the Mult. or Division property.  You should be able to conclude something about segment ZX.  Now use the first Given and you should have a good proof.  Altogether, four steps if you combine the three related Givens into one step.

#12)  Even more fun!!  I don't want to spoil it.  You should see a supplementary double-play; that's where I would start. By combining similar steps, I would get four steps.

#13)  Start with linear pairs, move into a supplementary triple-play.  With that conclusion, use either the Mult. or Div. property.  Again, combining similar steps with semi-colons, I would get six steps.

#16)  The reasons I would use for this proof, out of order, would include Division Property, LPP, Addition Property, Given, Diagram, Congruent Supplement Theorem, and Restate (you'll use <1 = <2 twice so you can call it Given or Restate).  Hardest proof in the packet.  Eight steps.

Hints for Addition & Subtraction Properties

Here are a few more tips for the proof packet:

# 3, 4, 5) Two-step proofs (the only thinking required is Reason #2 and  it'll either be the Addition Property or Subtraction Property)

# 7) Same as above but you have to come up with your own Conclusion (or Prove) statement. 

# 8)  Old stuff - If you combine all Givens, it'll be only 2 steps!

#10)  The way I did this in class is actually the old way... there's an easier method.  I get 5 steps, the last one using the subtraction property.

Remember, to use the subtraction property, you only need this format:
     1.  Get two "big" angles congruent.
     2.  Get two "little" angles congruent - as long as they're inside the big ones.
     3.  Put a brace around those two steps and conclude that the remaining little angles are congruent.

#11)  Four steps and the reasons are 1.  Given  2.  Definition of bisector  3.  Given   4.  ______________

#12)  Start with the trisection.  What does that mean??  It means that the segment is divided into three congruent segments.  Two of them are important in this problem.  You need to add them to other segments.  Should take four steps.

#13)  Almost identical to #10.  Remember that all right angles are congruent.  If you start with the perpend. step, you should follow that with a right angle step.  Throw in the other right angle statement that you're given and then state that they are congruent.  It will take two more steps to reach the Prove.  In total, six steps.

Video for Constructions

Hi Everybody,
I found a video on You Tube that should be helpful for you.  It covers most of the basic constructions that you've learned in class.  The man in the video does segment construction differently than we do -- he doesn't use a working line.  The particular construction that you should focus on is parallel line using alternate interior angles. 

About the trapezoid construction, you can simply construct the parallel line exactly the way he does.  I'll be giving you the lenghts of the bases by showing two segments.  After you construct the two parallel lines, you can make each of them congruent to "my" segments and then simply connect the endpoints.  You should have no trouble with that.

Enjoy the video.  Sorry I couldn't introduce you to my dog but I don't have access to a video camera at the moment.  Hope you're enjoying your weekend.

Mrs. Dant

Click here:  Geometric Construction

Sample Proofs for Packet

With the new theorems discussed in class, your proof packets should become much easier.  Below is a link that shows how you should use the new addition and subtraction properties.  Remember, they're not very different from the addition and subtraction properties we used in algebra proofs.

Here's the reasoning of these properties:

1.  Start with two equal "things"
2.  Add/Subtract the same thing (or equal things) to both
3.  Get equal results

Samples of New Addition/Subtraction Properties - Basic

Sample Proofs on Parallel Lines

Hi everybody,
If you click on the Sample link below, you should be taken to a Google Docs site to which I've uploaded two sample proofs.  I know that you have samples in your notes but I wanted to include these below for an extra resource.

Sample Flow Proofs - Chapter 3

I'll add to this periodically.  Don't hesitate to email me with questions.

Mrs. Dant

Proof Tips I

Hi Boys,
For the first page of proofs, you should be focusing on the supplementary/complementary "double and triple plays."  Remember, if you can get two supps or two comps into a proof, you'll probably end up with congruent angles.

Example:   1.  < A comp < B
                  2.  < C comp < D      ->  4.  < B = < C
                        3.  < A = < D
The reason for statement 4 would be:  Complements of congruent angles are congruent.

Page 1 
 - all double or triple plays

Page 2
- #9 is a simple warm-up to remind you what bisectors are --- 2 step proof!

- #10 should have a reason which states If two lines are perpendicular, they intersect to form right angles.  


- #11 - Start the proof with GJ bisects <FGH.  It will line up nicer and it's OK to have a triple play written "upside down."

- #16 Remember that definitions are reversible.  The definition of bisects is this:  If a ray bisects an angle, then it divides the angle into two congruent angles.   Use that definition?  Reverse it? Both????


 Don't give up easily - THINK HARD!!!