Proof: All radii of a circle are congruent, so AV AX, and since AZIVU and AY LXW, then AAZV ZA AYX are right triangles
by the
congruency theorem. The corresponding sides of the triangles, Zv and YX, 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
" AZ bisects VU and Ay bisects XW, SO VU = 2ZV and XW = 2YX. Therefore,
we can conclude that VU = XW, or
V XW.
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