Draw a line segment AB of length 8 cm. At each end of this line segment, draw a line perpendicular to AB. Are these two lines parallel?
Draw a line segment AB of length 8 cm. At each end of this line segment, draw a line perpendicular to AB. Are these two lines parallel?
Draw a line l and take a line segment AB of length 8 cm
Steps:
(i) Take a convenient radius with A as centre and draw an arc intersecting the line at points W and X.
(ii) With W and X as centres and radius greater than AW, construct two arcs intersecting each other at M.
(iii) Join AM and extend it in both directions to P and Q.
(iv) Take a convenient radius with B as centre and draw an arc intersecting the line at points Y and Z.
(v) With Y and Z as centres and a radius greater than YB, construct two arcs intersecting each other at N.
(vi) Join BN and extend it in both directions to S and R.
Let the lines perpendicular at A and B be PQ and RS, respectively.
∵ ∠QAB = 90° and ∠ABR = 90°
∴ ∠QAB = ∠ABR
When two parallel lines are intersected by a third line, the two alternate interior angles are equal.
∵ ∠QAB = ∠ABR
∴ PQ and RS are parallel.
Draw a line l and take a line segment AB of length 8 cm
Steps:
(i) Take a convenient radius with A as centre and draw an arc intersecting the line at points W and X.
(ii) With W and X as centres and radius greater than AW, construct two arcs intersecting each other at M.
(iii) Join AM and extend it in both directions to P and Q.
(iv) Take a convenient radius with B as centre and draw an arc intersecting the line at points Y and Z.
(v) With Y and Z as centres and a radius greater than YB, construct two arcs intersecting each other at N.
(vi) Join BN and extend it in both directions to S and R.
Let the lines perpendicular at A and B be PQ and RS, respectively.
∵ ∠QAB = 90° and ∠ABR = 90°
∴ ∠QAB = ∠ABR
When two parallel lines are intersected by a third line, the two alternate interior angles are equal.
∵ ∠QAB = ∠ABR
∴ PQ and RS are parallel.
