Question

examine the paragraph proof. which theorem does it offer proof for? according to the given information, jn and points l, n, m and o all lie on the same line. the measure of ∠lnm is 180° by the definition of a straight - angle. because ∠jni and ∠jnm are adjacent to one another, the angle addition postulate allows the measures of ∠jni and ∠jnm to equal the measure of ∠lnm. through the substitution property of equality, the measure of ∠jni plus the measure of ∠jnm equals 180°. since ∠jnm and ∠jhm are same - side interior angles, the measure of ∠jnm plus the measure of ∠jhm equals 180°. using substitution again, the measure of ∠jni plus the measure of ∠jhm equals the measure of ∠jnm plus the measure of ∠jhm. 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 ∠jni is the same as the measure of ∠jhm. 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

Explanation:

The proof uses properties of straight - line angles, adjacent angles, and angle - addition postulate, and shows that two non - adjacent angles are congruent. This is characteristic of the Alternate Interior Angles Theorem proof. It starts with a straight - line angle of 180 degrees, uses adjacent angle relationships and substitution to show that the alternate interior angles have equal measures, and thus are congruent.

Answer:

Alternate Interior Angles Theorem