Maharashtra Board Class 8 Maths Chapter 2 Parallel Lines and Transversals Set 2.3 Solutions

Question 1. Draw a line I. Take a point A outside the line. Through point A draw a line parallel to line I.
Solution:
Steps of construction:
(i) Draw a line I and take any point A outside the line.
(ii) Place a set-square, such that one arm of the right angle passes through A and the other arm is on line I.
(iii) Place the second set-square as shown in the figure such that the vertex of the right angle is at point A.
(iv) Hold the two set-squares in place and draw a line parallel to line I through the edge of the second set-square. Name the line as m.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र सेट-स्क्वायर और रूलर का उपयोग करके एक दी गई रेखा 'l' के समानांतर बिंदु 'A' से गुजरने वाली रेखा 'm' का निर्माण दर्शाता है। इसमें दो सेट-स्क्वायर को संरेखित करके समानांतर रेखा खींची गई है। Line m is the required line parallel to line I and passing through point A.
Answer: Construction steps as described, resulting in line m parallel to line I through point A.
In simple words: To draw a parallel line, use two set-squares. Place one set-square along the given line and the other touching the point through which the parallel line needs to pass, then slide and draw.

🎯 Exam Tip: Ensure precise alignment of set-squares for accurate parallel line construction. Clearly label all lines and points as specified in the question.

Question 2. Draw a line I. Take a point T outside the line. Through point T draw a line parallel to line I.
Solution:
Steps of construction:
(i) Draw a line I and take any point T outside the line.
(ii) Place a set-square, such that one arm of the right angle passes through T and the other arm is on line I.
(iii) Place the second set-square as shown in the figure such that the vertex of the right angle is at point T.
(iv) Hold the two set-squares in place and draw a line parallel to line I through the edge of the second set-square. Name the line as m.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र सेट-स्क्वायर और रूलर की सहायता से एक दी गई रेखा 'l' के समानांतर बिंदु 'T' से गुजरने वाली रेखा 'm' के निर्माण की विधि को दर्शाता है। इसमें दो सेट-स्क्वायर का सही उपयोग करके समानांतर रेखा खींची गई है। Line m is the required line parallel to line I and passing through point T.
Answer: Construction steps as described, resulting in line m parallel to line I through point T.
In simple words: The method involves using set-squares to create a line parallel to a given line, passing through a specific external point.

🎯 Exam Tip: Practice accurate drawing of perpendiculars and parallel lines. Clearly mark the given point and the constructed parallel line for full marks.

Question 3. Draw a line m. Draw a line n which is parallel to line m at a distance of 4 cm from it.
Solution:
Steps of construction:
(i) Draw a line m and take any two points M and N on the line.
(ii) Draw perpendiculars to line m at points M and N.
(iii) On the perpendicular lines take points S and T at a distance 4 cm from points M and N respectively.
(iv) Draw a line through points S and T. Name the line as n.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक रेखा 'm' के समानांतर एक और रेखा 'n' के निर्माण को दर्शाता है, जो रेखा 'm' से 4 सेमी की दूरी पर है। इसमें रेखा 'm' पर दो बिंदु M और N लेकर, उन पर लंब खींचे गए हैं और फिर उन लंबों पर 4 सेमी की दूरी पर बिंदु S और T अंकित करके रेखा 'n' को खींचा गया है। Line n is parallel to line m at a distance of 4 cm from it.
Answer: Construction steps as described, resulting in line n parallel to line m at a 4 cm distance.
In simple words: To draw a parallel line at a specific distance, draw perpendiculars from two points on the original line, mark the required distance on these perpendiculars, and connect the marked points.

🎯 Exam Tip: Use a ruler and protractor/set-square for precise measurement of 4 cm and drawing of perpendiculars. Accuracy in measurement is crucial for this type of construction.