Given: Circle O; Angle A intercepts Arc B C D; Angle D intercepts Arc B C Prove: Angle A is-congruent-to Angle D Circle O is shown. Angles A and D intercept arc B C. Angles B and C intercept arc A 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.
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