Question

5.
Prove that the bisectons of any pair of Interior angles
perpendicular each other then the lines are
parallel
other​

Answer 1

true. bisector of each pair of integer angel perpendicular each other then the lines are parallel

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Answer 2

Answer:

here is your answer

Step-by-step explanation:

The interior angles on the same side of the transversal (called consecutive interior angles) are supplementary (they sum to 180 degrees). Call these angles a and b.

a+b=180

o

Now divide both sides by 2:

2a+ 2b

=90 o

2a and 2b

are just the halves of a and b formed by their bisectors.

These bisectors intersect, forming the legs of a triangle with the transversal being the third side.

The interior angles of this triangle are

2a , 2b

and the angle formed by the intersection of the bisectors.

Call this as ∠c.

Since the sum of the interior angles of a triangle is 180 degrees:

2a + 2b +c=180 o

Since you know

2a + 2b =90 o

90 o +∠c=180 o

⇒∠c=90 o

So the bisectors are perpendicular.