Question

inscribed angles
given: circle m with inscribed ∠kjl and congruent radii jm and ml.
prove: m∠mjl = ½ (m⌢kl)

1. m∠kml = 2 (m∠mjl) | 6. substitution property
2. m⌢kl = m∠kml | 7. central ∠ of △ and intercepted arc have same measure
3. m⌢kl = 2 (m∠mjl) | 8. ?
4. ½ (m⌢kl) = m∠mjl | 9. multiplication property of equality

what is the missing reason in step 8?

options:
substitution property
reflexive property
second corollary to the inscribed angles theorem
base angles theorem

Explanation:

Step 7 states \(m\widehat{KL} = m\angle KML\) (central angle equals intercepted arc measure). Step 6 states \(m\angle KML = 2(m\angle MJL)\). To get step 8 (\(m\widehat{KL} = 2(m\angle MJL)\)), we replace \(m\angle KML\) in step 6 with \(m\widehat{KL}\) from step 7, which uses the substitution property of equality.

Answer:

substitution property