Two parallel lines are intersected by a transversal. Prove: Angle bisectors of the same side interior angles are perpendicular.
1 answer:
Answer:
The answer is given below
Step-by-step explanation:
From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.
The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠BYZ and ∠DZY are interior angles.
∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)
∠BYZ/2 + ∠DZY/2 = 180/2
∠BYZ/2 + ∠DZY/2 = 90°
In ΔOYZ:
∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).
But ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2
∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180
90 + ∠YOZ = 180
∠YOZ = 180 - 90
∠YOZ = 90°
Therefore Angle bisectors of the same side interior angles are perpendicular.
You might be interested in
What we know here is that all 2500 shares together are worth 100 000 dollars in total. (it's 100 000.00 actually, but we can ignore the part after the point, as it's equal to 0).
This means that each of the shares is valid the whole sum divided by the number of shares, that is:
(first i divided both denominator and numerator by 100)
So each value is worth 40 dolars.
This means that each of the shares is valid the whole sum divided by the number of shares, that is:
(first i divided both denominator and numerator by 100)
So each value is worth 40 dolars.