Euclid Book 1, Proposition 2
- Author:
- L. Marizza A. Bailey, Esther Gruenhut
- Topic:
- Geometry
To place a straight line equal to a given straight line with one end at a given point.
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Summarize Euclid, Proposition 2
In your own words, what is Euclid's Proposition 2?
Step 1
What is the first step of the proof?
Step 2
What is the second step of the proof?
Step 3 - 5
In Steps 3 - 5, Euclid creates another circle. What do you know about the relationship between BE and BC?
Steps 6 and 7
In Steps 6 and 7, Euclid constructs a point, F. Why is DF = DE?
Segment Addition Postulate 1
We know DF = DE, and DA+AF = DB+BE. Why is DA = DB?
Segment Addition Postulate 2
We know DF = DE, DA + AF = DB + BE, and DA = DB. Explain how this tells you that AF = BE.
Revisit "Steps 3 - 5" question and the previous question
In "Steps 3- 5" you concluded that BE = BC. In the previous question, you concluded that AF = BE. What property allows you to conclude that AF = BC?
Why you won...
Why is AF the segment that Euclid was trying to construct in Proposition 2.