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