Question

If two parallel lines are intersected by a transversal then prove that the bisectors of the interior angles on same side of transversal intersect each other at right angles

Answer 1

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 the triangle 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.  

Answer 2

Answer:

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