Examine the paragraph proof. Which theorem does it offer proof for? Prove JNL HMN According to the given information, JK || HI and points L. N. M and O all lie on the same line. The measure of LNM 180° by the definition of a straight angle. Because LJNL and LJNM are adjacent to one another, the Angle Addition Postulate allows the measure of ZJNL and ZJNM to equal the measure of LNM. Through the Substitution Property of Equality, the measure of LJNL plus the measure of LJNM equals 180° Since 2JNM and HMN are same-side interior angles, the measure of LJNM plus the measure of HMN equals 180° Using substitution again, the measure of ZJNL plus the measure of LJNM equals the measure of LNM plus the measure of HMN. Finally, the Subtraction Property of Equality allows the measure of JNM to be subtracted from both sides of the equation. The result is that the measure of LJNL is the same as the measure of HMN. Because their angle measures are equal, the angles themselves are congruent by the definition of congruency Alternde Interior Angles Theorem Corresponding Angles Theorem Vertical Angles Theorem Same-Side Intenor Angles Theorem