S.O.S. Mathematics CyberBoard

[integral0]

When you are proving proofs in geometry, is it necessary to identify every single property along the way or can I skip over some small (non-important steps).

For example, I was doing a problem where I had an angle that was bisected. All of the rays of the angle (2) and the bisector (1) were then extended the other direction. Then the angles (4) were labeled 1,2,3,4. One had to prove the m<AOB = m<EOf (main large angles). So what I did was I said that the def. of bisector angle enables angles 3 and 4 to be congruent. Then I said that the vertical angles of 3 and 1, 2 and 4, and m<AOB and m<EOf were also equal because of the def. of vertical angles. So there was my proof.

However . . . the book had the substitution property involved and transitive property involved which are understandable but not really necessary (at least I think).

What do you have to say?

[integral0]

odd . . . no one has responded

[integral0]

thanks Soroban

[jpmcgdogm]

Transitive Property of Equality: if a = b and b = c, then a = c

Substitution Property of Equality: if a = b, then a can be substituted for b in any equation or inequality

vertical angles theorem
If two angles are vertical angles, then they have equal measures

I wouldn't say that your line of reasoning is wrong. Many times
while working with proofs in geometry there is usually more than one
way to get from your given to what you have to prove. I listed the properties
that you mentioned and then the vertical angles theorem so if you analyze them you may find that you can accomplish the same thing either way.

I hope that brings you some enlightenment.