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 of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. That sum can equal the length of the third side only in the case of a degenerate triangle, one with collinear vertices. It is not possible for that sum to be less than the length of the third side. A triangle with three given positive side lengths exists if and only if those side lengths satisfy the triangle inequality. Three given angles form a non-degenerate triangle (and indeed an infinitude of them) if and only if both