Given: Circle M with inscribed Angle K J L and congruent radii JM and ML Prove: mAngle M J L = One-half (measure of arc K L) Circle M is shown. Line segment J K is a diameter. Line segment J L is a secant. A line is drawn from point L to point M. What is the missing reason in step 8? Statements Reasons 1. circle M with inscribed ∠KJL and congruent radii JM and ML 1. given 2. △JML is isosceles 2. isos. △s have two congruent sides 3. m∠MJL = m∠MLJ 3. base ∠s of isos. △are ≅ and have = measures 4. m∠MJL + m∠MLJ = 2(m∠MJL) 4. substitution property 5. m∠KML = m∠MJL + m∠MLJ 5. measure of ext. ∠ equals sum of measures of remote int. ∠s of a △ 6. m∠KML =2(m∠MJL) 6. substitution property 7. Measure of arc K L = measure of angle K M L 7. central ∠ of △ and intercepted arc have same measure 8. Measure of arc K L = 2 (measure of angle M J L) 8. ? 9. One-half (measure of arc K L) = measure of angle M J L 9. multiplication property of equality reflexive property substitution property base angles theorem second corollary to the inscribed angles theorem