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.