Examine the paragraph proof. Which theorem does it offer proof for?
Segments JK and HI are parallel, segment LO intersects segment JK at point N, segment LO intersects segment HI at point M, and points N and M are between points L and O on segment LO.
Prove: ∠JNL ≅ ∠HMN
According to the given information, segment JK is parallel to segment 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 ∠JNL and ∠JNM are adjacent to one another, the Angle Addition Postulate allows the measure of ∠JNL and ∠JNM to equal the measure of ∠LNM. Through the Substitution Property of Equality, the measure of ∠JNL plus the measure of ∠JNM equals 180°. Since ∠JNM and ∠HMN are same-side interior angles, the measure of ∠JNM plus the measure of ∠HMN equals 180°. Using substitution again, the measure of ∠JNL plus the measure of ∠JNM equals the measure of ∠JNM 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 ∠JNL is the same as the measure of ∠HMN. Because their angle measures are equal, the angles themselves are congruent by the definition of congruency.
Alternate Interior Angles Theorem
Corresponding Angles Theorem
Vertical Angles Theorem
Same-Side Interior Angles Theorem