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If two parallel lines are intersected by a transversalthen the bisectors of the interior angles form a- |
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Answer» From the property of interior angle of same side. we get sum of interior angles on same is 180 degrees. Let p and q are the interior angles on same side, such that p+q=180. Now consider thetriangle formed by transversal line, the two angular bisectors of interior angles of p and q. we can find two angles as p/2 and q/2. SInce there are angular bisectors. Let the third angle be 't'. As we know sum of angles in a triangle is 180. then we get p/2+q/2+t=180 ⇒1/2(p+q)+t=180 ⇒1/2(180)+t=180 ⇒90+t=180 ⇒t=90. Since t is the angle intersected by two angular bisectors of interior angles on same side. They intersect at right angles. Hence proved. |
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