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?


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
Measure of arc K L = 2 (measure of angle M J L)

8. ?
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


  1. For this circle M, the missing reason in step 8 is substitution property.

    What is the theorem of intersecting chord?

    The theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.

    What is the substitution property?

    The substitution property states that assuming x, y, and z are three (3) quantities, and if x is equal to 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) are equal to each other by the same rule.
    From step 6, we have:
    m∠KML = 2(m∠MJL) ⇒ substitution property.
    By the same substitution property, we have:
    Step 8: m∠KL = 2(m∠MJL)
    Read more on substitution property here:


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