Statements Reasons 1. circle cap o ; angle cap A intercepts overarc BC ; angle cap d intercepts overarc BC 1. given 2. m angle cap A is equal to 1 half times open paren m overarc BC close paren 2. ? 3. m angle cap d is equal to 1 half times open paren m overarc BC close paren 3. ? 4. m angle cap A is equal to m angle cap d 4. substitution property 5. angle cap A is congruent to angle cap d 5. definition of congruent angles Two statements are missing reasons. What reason can be used to justify both statements 2 and 3 ?
Answer
A
third corollary to the inscribed angles theorem
B
central angle of a triangle has the same measure as its intercepted arc.
C
angle formed by a tangent and a chord is half the measure of the intercepted arc.
D
inscribed angles theorem
Explanation
The inscribed angles theorem says that the measure of an inscribed angle is one-half the measure of its intercepted arc. Since both angle A and angle d intercept arc BC, each has measure one-half of the measure of arc BC. Therefore, the reason for both statements is the inscribed angles theorem.
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