Distance from a point to a line the perpendicular "R". Draw the vertical line through "P" and label its intersection with the given line "S". At any point "T" on the line, draw a right triangle "TVU" whose sides are horizontal and vertical line segments with hypotenuse "TU" on the given line and horizontal side of length |"B"| (see diagram). The vertical side of ∆"TVU" will have length |"A"| since the line has slope -"A"/"B". ∆"PRS" and ∆"TVU" are similar triangles, since they are both right triangles and ∠"PSR" ≅ ∠"TUV" since they are corresponding angles of a transversal to the parallel lines "PS" and "UV" (both
Fermat's right triangle theorem and the other is odd. Therefore, both formula_39 and formula_40 are even, one of which is divisible by 4. From these two numbers Fermat derives two more numbers formula_41 and formula_42, one of which is even by the previous sentence. Because formula_43 is a square, formula_44 and formula_45 are the legs of another primitive Pythagorean triangle whose area formula_46. Since formula_27 is itself a square and since formula_48 is even, formula_49 is a square. Thus, any Pythagorean triangle with square area leads to a smaller Pythagorean triangle with square area, completing the proof. Fermat's right triangle theorem Fermat's right triangle