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
Triangle squares. An obtuse triangle has only one inscribed square, with a side coinciding with part of the triangle's longest side. Within a given triangle, a longer common side is associated with a smaller inscribed square. If an inscribed square has side of length "q" and the triangle has a side of length "a", part of which side coincides with a side of the square, then "q", "a", the altitude "h" from the side "a", and the triangle's area "T" are related according to The largest possible ratio of the area of the inscribed square to the area of the triangle