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Let l 1 and l 2 be two lines cut by transversal t such that 2 and 4 are supplementary as shown in the figure.
Same side interior angles are congruent math. From the same side interior angles definition the pairs of same side interior angles in the above figure are. 1 and 4 2 and 3. The sides of the angles do not need to have the same length or open in the same direction to be congruent they only need to have equal measures. Congruent angles are angles that have the same measure.
Same side interior angles are supplementary. Since 2 and 4 are supplementary then 2 4 180. Interior angles are formed when two parallel lines are intersected by another line forming angles at each intersection between the parallel lines. The converse of same side interior angles theorem proof.
The measure of angles a and b above are 57 so a b and a b. The measure of angles a and b above are both 34 so angles a and b are congruent or a b where the symbol means congruent. By the definition of a linear pair 1 and 4 form a linear pair.
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