# 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.
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.