Given: circle o; angle a intercepts arc b c d ; angle d intercepts arc b c prove: angle a is-congruent-to angle d two statements are missing reasons. what reason can be used to justify both statements 2 and 3? statements reasons 1. circle o; angle a intercepts arc b c. angle d intercects arc b c 1. given 2. measure of angle a = one-half (measure of arc b c) 2. ? 3. measure of angle d = one-half (measure of arc b c) 3. ? 4. measure of angle a = measure of angle d 4. substitution property 5. angle a is-congruent-to angle d 5. definition of congruent angles inscribed angles theorem third corollary to the inscribed angles theorem central angle of a triangle has the same measure as its intercepted arc. angle formed by a tangent and a chord is half the measure of the intercepted arc.