Proof: all radii of a circle are congruent, so , and since and , then are right triangles by the congruency theorem. the corresponding sides of the triangles, and , are congruent, so zv = yx. thus, we know that 2zv = 2yx by the multiplication property of equality. by a congruency theorem that states, "if a diameter of a circle is perpendicular to a chord, then the " bisects and bisects , so vu = 2zv and xw = 2yx. therefore, we can conclude that vu = xw, or . a. hl (hypotenuse-leg) . . diameter bisects the chord and its other chord b. sss (side-side-side) . . diameter bisects the arc and its measurement c. hl (hypotenuse-leg) . . diameter bisects the chord and its arc d. asa (angle-side-angle) . . chord but not the diameter