In quadrilateral abcd, aabd: aacd=1: 2. if bh is an altitude in △abd and cl is an altitude in △acd, find bh: cl. answer with statement reason format

For the given altitudes, CD is the base . . . . the base is the side opposite the vertex to which the altitude is measured

For ∆ABD, the area is (1/2)(AD)(BH) . . . . formula for area of a triangle

For ∆ACD, the area is (1/2)(AD)(CL) . . . . formula for area of a triangle

The ratio of ((1/2)(AD)(BH)) / ((1/2)(AD)(CL)) is 1/2 . . . . given (& substitution property of equality)

The simpified form of this expression is BH/CL = 1/2 . . . . properties of arithmetic

In ratio form, this expression is BH : CL = 1 : 2 . . . . equivalence of ratio expressions