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

Mark this and return

circleM, the missing reason in step 8 issubstitution property.## What is the theorem of intersecting chord?

intersecting chordstates that when two (2) chordsintersectinside acircle, the measure of the angle formed by thesechordsis equal to one-half (½) of the sum of the two (2) arcs it intercepts.## What is the

substitution property?substitution propertystates that assuming x, y, and z are three (3) quantities, and if x isequalto y (x = y) based on a rule and y is equal to z (y = z) by the same rule, then, x and z (x = y) areequalto each other by the same rule.substitution property, we have:substitution propertyhere: https://brainly.com/question/9260811