<prompt> Netefatsa hore haeba AB e le parallelogram, joale A B 180.nan  <response>: Instruction in English: Prove that if AB is a parallelogram, then A B 180. . Response in English: If AB is a parallelogram, this means that the opposite sides are parallel to each other. Lets say that side AB is parallel to side CD, and side BC is parallel to side AD. Since these pairs of sides are parallel, this indicates the presence of alternate interior angles between them. Alternate interior angles occur between two parallel lines when they are cut by a third intersecting line, and they are congruent. In our parallelogram, the angles created by the intersection of lines BC and AD are alternate interior angles. Therefore, A is congruent to C, and B is congruent to D.We know that the sum of the interior angles of any quadrilateral is 360. So, A B C D 360. Since C is congruent to A, and D is congruent to B, we can substitute these angles to obtain: A B A B 360.By simplifying this expression, we find that 2A B 360. Solving for A B, we find that A B 180.Therefore, we have shown that if AB is a parallelogram, then A B 180. . Response in Sesotho: Haeba AB e le parallelogram, sena se bolela hore mahlakore a fapaneng a bapile. Ha re re lehlakore la AB le bapile CD ea lehlakore, me lehlakore la BC le bapa le AD. Kaha lipara tsena tsa mahlakore li bapile, sena se bontša boteng ba li-angles tse fapaneng tsa ka hare lipakeng tsa tsona. Li-angles tse ling tse ka hare li etsahala pakeng tsa mela e meli e bapileng ha li sehoa ke mola oa boraro o intersecting, me lia lumellana. Papisong ea rona, li-angles tse entsoeng ke mateano a litsela tsa BC le AD ke li-angles tse ka hare tse fapaneng. Ka hona, A e lumellana le C, me B e tšoana le D. Rea tseba hore kakaretso ea li-angles tse ka hare tsa quadrilateral efe kapa efe ke 360. Kahoo, A B C D 360. Kaha C e lumellana le A, me D e lumellana le B, re ka fetola li-angles tsena ho fumana: A B A B 360. Ka ho nolofatsa polelo ena, re fumana hore 2A B 360. Ha re rarolla A B, re fumana hore A B 180. Ka hona, re bontšitse hore haeba AB e le parallelogram, joale A B 180 . 