Parallel lines cut by diagonals and equal parallelograms
Consideration 34; alternate interior angles proved by the fourth and the twenty-sixth
A sparse geometry page on parallels and parallelograms. Pairs of parallel lines, one joined by a vertical segment, and parallelograms split by a single diagonal are drawn with alternate interior angles marked by dots as equal. An encircled number, 34, labels the consideration. The relations among the figures are justified 'with, by the fourth,' 'with the fourth,' and 'with 26,' citing Euclid's propositions, several drawn over faint pencil constructions.
On this page
Alternate interior angles of parallels are equal
Two vertical parallels crossed by a diagonal have their alternate interior angles marked as similar by dots. Parallelograms divided by one diagonal are justified with, by the fourth, showing the equal halves.
Rectangles from parallels, proved by the fourth and twenty-sixth
Three views of parallels crossed by a diagonal include one where a rectangle is formed by adding vertical segments, with opposite interior angles dotted. The equalities are proved with the fourth and with 26.