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
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