Draw a line segment AB of length 5 cm. At A and B, construct lines perpendicular to AB. Also, draw the perpendicular bisector of AB. Are these three lines parallel to each other? Justify your answer.
Answers
Answer:
Here the length of AB = 5cm
DA is perpendicular to AB.
EB is perpendicular to AB.
Two lines perpendicular to same line are parallel to each other.
Also \angle1 =\angle 3 = 90^{o}∠1=∠3=90o
So \angle1 + \angle3 = 180^{o}∠1+∠3=180o
If the sum of co interior angles = 180°, the lines are parallel.
Hence AD || BE
Now we construct the perpendicular bisector of AB which intersects AB at C
Again
\angle1= \angle2 = 90^{o}∠1=∠2=90o
So
\angle1 + \angle2 = 180^{o}∠1+∠2=180o
We know If the sum of co interior angles = 180°, the lines are parallel.
Hence AD || CF
Now BE ||AD || CF
Hence all the three lines are parallel to each other.
Step-by-step explanation:
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ANSWER:
- LENGTH OF AB = 5CM
- AD IS PERPENDICULAR TO AB
- EB IS PERPENDICULAR TO AB
- TWO LINES PERPENDICULAR TO THE SAME LINE ARE ALWAYS PARALLEL TO EACH OTHER
- ALSO
ANGLE 1= ANGLE 3 = 90°
ANGLE 1 + ANGLE 3 = 180°
- SUM OF COOINTERIOR ANGLES IS 180° SO IT'S PARALLEL
- SO ALL THREE LINES ARE PARALLEL TO EACH OTHER
