Question

If two line are parallel then prove that any pair of bisectors of their alternate interior angle is also parallel

Answer 1

for parallel lines some conditions are applied. ere are;
1) showing a pair of corresponding angles are equal.
2) showing a pair of alternate interior angles are equal.
3) In a plane, showing both lines are perpendicular to the same line.
4) showing both lines are parallel to a third line.
5) showing a pair of interior angles on the same side of the transversal are supplementary.

Answer 2

Answer:

Any pair of bisectors of the alternate interior angle is also parallel.

Step-by-step explanation:

Let AB and CD are the two parallel lines, and MN be the transversal line drawn across the parallel lines.

• The angles that are interior and on either side of the transversal line are called alternate interior angles.
• The measures of alternate interior angles are equal.
• Two pairs of alternate interior angles are formed, $\angle CYX~ \&~\angle BXY$ and $\angle DYX~ \&~\angle AXY$.
• Consider a pair of alternate interior angles, $\angle CYX~ \&~\angle BXY$
• Draw bisectors to these two angles, let them XX' and YY'.
• Since these are the bisectors, they divide the equal angles into equal halves.
• Hence we can say, $\angle YXX'~ =~\angle XYY'$.
• These angles represent the alternate interior angles for XX' and YY' with MN as a transversal line.
• Therefore, XX' is parallel to YY'.

Hence, we can say that any pair of bisectors of the alternate interior angle is also parallel.

For more info

https://brainly.in/question/26494841

https://brainly.in/question/21687253