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Euclid Book 1, Proposition 2

To place a straight line equal to a given straight line with one end at a given point. Use the scroll bar to unfold Euclid's construction.

Click the scroll bar and click the right and left arrow keys to make one move at a time.

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.