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Source — Euclid's Elements, encoded as an rrxiv paper

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I.32 Proposition I.32

In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.

Proof

Apply I.31 to draw a parallel through the apex; apply I.29 twice and Common Notion 2.

Figure

$Proposition I.32. Drawing $DE$ through $C$ parallel to $AB$ makes $\angle DCA = \angle CAB$ (alternate, I.29) and $\angle ECB = \angle ABC$ (alternate, I.29); the straight angle at $C$ then sums the three interior angles of $\triangle ABC$ to two right angles.$

Proposition I.32. Drawing

D E

through

C

parallel to

A B

makes

∠ D C A = ∠ C A B

(alternate, I.29) and

∠ E C B = ∠ A B C

(alternate, I.29); the straight angle at

C

then sums the three interior angles of

△ A B C

to two right angles.

lines 74–74 in main.tex

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