fundamentals
defining and constructing the relationships of points, lines, circles
- definitions
- common notions
- postulates
- propositions
- construct an equilateral triangle on a segment
- construct equal segments by extension
- construct equal segments by section
- triangles with equal sides have equal angles
- The base angles of an isosceles triangle are equal
- when two angles of a triangle are equal, so are the subtended sides
- the sides of a triangle are uniquely related to the position of the vertexes
- triangles with equal sides have equal angles
- bisect angle
- bisect segment
- construct perpendicular from point on line
- construct perpendicular from point not on line
- angles from intersecting lines equal two right angles (on one side)
- adjacent angles equal to two right angles make a line
- opposing angles of intersecting lines are equal
- the sum of any two angles of a triangle is less than two right angles
- the greater side of a triangle subtends the greater angle
- the greater angle of a triangle is subtended by the greater side
- any two sides of a triangle are greater than the remaining side
- Proposition I.21
- construct a triangle from three segments
- construct a given angle on a given segment
- similar triangles
- similar triangles
- similar triangles
- the angles produced from a line intersecting parallel lines are equal
- similar angles from line intersecting parallels
- parallel angles
- parallels are parallel to each other
- construct a parallel to a line through a point
- similar triangles
- similar angles on parallels
- parallelogram angles
- parallelogram equality
- parallelogram equality
- triangles in parallels equality
- triangle and parallels equality
- triangles and parallels
- triangles and parallels
- parallelograms and triangles
- construct a parallelogram equal to a given triangle on a given angle
- equality of parallelogram complements
- construct a parallelogram on a segment equal to a given triangle
- construct a parallelogram equal to a given polygon on a given angle
- construct a square
- the squares on the sides of a right triangle are equal to the square on the hypotenuse
- a triangle is right if the sum of squares of two sides equals the square on the remaining