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December 30th, 2017, 01:45 PM  #1 
Member Joined: Nov 2016 From: USA Posts: 36 Thanks: 1  Reason to give in a proof for this step?
Given AB is a line segment (180 degrees for a straight angle) Given angle AWZ is congruent to angle YWB What is the reason to provide in a proof that angle AWY = angle ZWB? Thank you. 
December 30th, 2017, 02:11 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,934 Thanks: 2208 
Let AAP denote Angle Addition Postulate, which is a key geometrical result you need to use. m$\small\angle$AWZ = m$\small\angle$AWY + m$\small\angle$YWZ (AAP) m$\small\angle$YWB = m$\small\angle$YWZ + m$\small\angle$ZWB (AAP) You also need to know that congruent angles have equal measure. The rest is just algebra. 
December 30th, 2017, 02:45 PM  #3  
Member Joined: Nov 2016 From: USA Posts: 36 Thanks: 1  Quote:
In a formal proof, is it sufficient to write in the proof: STATEMENT....................................REASO N 1.AB is a line segment......................1.Given 2.Angle AWZ = Angle YWB................2.Given 3.Angle AWY = Angle ZWB................3.Angle Addition Postulate Or, do I need to show the calculations in the proof? like this: STATEMENT......................................... ..............REASON 1. AB is a line segment........................................Giv en 2. Angle AWZ = Angle YWB..................................Given 3. Angle AWY + Angle YWZ = Angle YWZ + ZWB .................... Angle YWZ......Angle YWZ Angle AWY = Angle ZWB....................................Angle Addition Postulate  
December 30th, 2017, 05:08 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,934 Thanks: 2208 
You should omit the first line, as the fact that AB is a line segment isn't used. Your first "proof" doesn't give enough detail. You could be using m$\small\angle$AWB = m$\small\angle$AWY + m$\small\angle$YWB (AAP) m$\small\angle$AWB = m$\small\angle$ZWB + m$\small\angle$AWZ (AAP) angle AWZ is congruent to angle YWB (given) m$\small\angle$AWZ = m$\small\angle$YWB (definition of congruent angles) which is also a valid approach. You should then show the calculations and give the precise reasons for the algebraic steps. For example, you would probably use certain properties of equality, such as the subtractive property, the transitive property or the substitution property. 

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