Two right triangles are similar if an acute angle of one is congruent to an acute angle of the other. A line parallel to a side of a triangle cuts off a triangle similar to the given triangle. Triangles similar to the same triangle are similar to each other. The altitude to the hypotenuse of a right triangle divides it into two triangles which are similar to the given triangle and to each other. Triangles are similar if their sides are respectively parallel to each other.
Triangles are similar if their sides are respectively perpendicular to each other.
Extending a Basic Proportion Principle Corresponding sides of similar triangles are in proportion. Corresponding segment of similar triangles are in proportion. Corresponding segments of similar polygons are in proportion. If two chords intersect within a circle, the product of the length of the segments of one chord equals the produce of the lengths of the segments of the other. If a tangent and a secant intersect outside a circle, the tangent is the mean proportional between the secant and its external segment.