# Category:Euclid Book I

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These proofs can all be found in Book $\text {I}$ of Euclid's *The Elements*.

The specific form of these has been adapted from Sir Thomas L. Heath's *Euclid: The Thirteen Books of The Elements: Volume 1, 2nd ed.*

## Pages in category "Euclid Book I"

The following 60 pages are in this category, out of 60 total.

### C

- Complements of Parallelograms are Equal
- Construction of Equal Angle
- Construction of Equal Straight Line
- Construction of Equal Straight Lines from Unequal
- Construction of Equilateral Triangle
- Construction of Parallel Line
- Construction of Parallelogram equal to Triangle in Given Angle
- Construction of Parallelogram in Given Angle equal to Given Polygon
- Construction of Parallelogram on Given Line equal to Triangle in Given Angle
- Construction of Perpendicular Line
- Construction of Square on Given Straight Line
- Construction of Triangle from Given Lengths
- Converse Hinge Theorem

### E

- Equal Alternate Angles implies Parallel Lines
- Equal Corresponding Angles implies Parallel Lines
- Equal Corresponding Angles or Supplementary Interior Angles implies Parallel Lines
- Equal Sized Triangles on Equal Base have Same Height
- Equal Sized Triangles on Same Base have Same Height
- External Angle of Triangle equals Sum of other Internal Angles
- External Angle of Triangle equals Sum of other Internal Angles/Historical Note
- External Angle of Triangle Greater than Internal Opposite

### G

### L

### P

- Parallelism implies Equal Alternate Angles
- Parallelism implies Equal Alternate Angles, Corresponding Angles, and Supplementary Interior Angles
- Parallelism implies Equal Corresponding Angles
- Parallelism implies Supplementary Interior Angles
- Parallelism is Transitive
- Parallelogram on Same Base as Triangle has Twice its Area
- Parallelograms with Equal Base and Same Height have Equal Area
- Parallelograms with Same Base and Same Height have Equal Area
- Perpendicular through Given Point
- Pythagoras's Theorem/Classic Proof

### S

### T

- Triangle Angle-Side-Angle and Side-Angle-Angle Equality
- Triangle Angle-Side-Angle Equality
- Triangle Side-Angle-Angle Equality
- Triangle Side-Angle-Side Equality
- Triangle Side-Side-Side Equality
- Triangle with Two Equal Angles is Isosceles/Proof 1
- Triangles with Equal Base and Same Height have Equal Area
- Triangles with Same Base and Same Height have Equal Area
- Two Angles making Two Right Angles make Straight Line
- Two Angles of Triangle Less than Two Right Angles
- Two Angles on Straight Line make Two Right Angles
- Two Lines Meet at Unique Point
- Two Straight Lines make Equal Opposite Angles