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 theore
