The idea of equal alternate angles is used to construct what
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Answer:
Have you ever thought how to construct a line parallel to a given line and a point not on it? Well, we can use alternate angles in a transversal diagram to draw, we can also use corresponding angles to do the construction.
Construction of a line parallel to a given line at a given distance
Construct a parallel line to a given line l at a distance of 4.5 cm (using compass and ruler only).
Steps of construction:
Draw a line l and mark two points A and B on it.
With A as centre and suitable radius, draw an arc to intersect the line l at M and N.
With M as centre and more than half of AM as radius, draw an arc above line l.
With N as centre and same radius, draw an arc to intersect the previous arc at O.
Join ray AO. Ray AO is perpendicular to the line l.
Similarly draw ray BW perpendicular to line l by repeating steps 2 to 5.
With A as centre and 4.5 cm as radius, draw an arc to intersect ray AO at P.
With B as centre and 4.5 cm as radius, draw an arc to intersect ray BW at X.
Draw a line m through the points P and X.
Construction of parallel lines based on the concept of alternate angles.
Draw a line XY = 8 cm. Mark a point A above it and drawAP || XY
Steps of constructions:
Draw a line segment XY = 8 cm.
Mark a point A above XY and join XA
With X as centre and any radius, draw an arc to intersect XY at I and XA at J.
Now with A as centre and same radius, draw an arc to intersect XA at Q.
Place the pointed tip of the compass at I and adjust the opening so that the pencil tip is at J.
Now with the same opening and with Q as centre, draw an arc to intersect the previous arc at P.
Join AP to draw a line m.
Construction of parallel lines using the concept of corresponding angles
Draw a line segment AB = 8 cm. Draw a line XY parallel to AB following the inverse property of the corresponding angles.
Steps of construction:
Draw a line segment AB = 8 cm
Mark a point C above AB and a point D on AB
Join CD
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