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December 30th, 2017, 02:45 PM   #1
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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?

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December 30th, 2017, 03:11 PM   #2
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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.
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December 30th, 2017, 03:45 PM   #3
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Quote:
Originally Posted by skipjack View Post
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.
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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
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December 30th, 2017, 06:08 PM   #4
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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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