Question 15
Construct 4 pairs of parallel lines in different orientations.
We can draw parallel lines by making sure that corresponding angles are equal when a transversal line cuts them.
Step 1 — Draw a line and a transversal
- Let us draw a straight line.
- We will name this line AB.
- Now, draw another line.
- This line should cut line AB.
- Let us name this line CD.
- Line CD is a transversal.
- Let them meet at point E.
Step 2 — Choose a point for the new line
- Choose any point on line CD.
- This point should not be E.
- Let us call this point P.
- We want to draw a line through P.
- This new line will be parallel to AB.
Step 3 — Copy the angle at E
- Place your compass point at E.
- Draw an arc that cuts line AB at F.
- The arc also cuts line CD at G.
- Keep the compass opening the same.
- Place the compass point at P.
- Draw another arc.
- This arc cuts line CD at H.
- Now, measure the distance between F and G.
- Use your compass to measure this.
- Place the compass point at H.
- Draw an arc that cuts the second arc.
- Let this new intersection point be I.
Step 4 — Draw the parallel line
- Draw a straight line.
- This line must pass through point P.
- It must also pass through point I.
- Extend this line on both sides.
- Let us name this new line JK.
- Line JK is parallel to line AB.
- Angle PEB and angle CPK are corresponding angles.
- We made these angles equal.
- So, lines AB and JK are parallel.
Step 5 — Draw more parallel pairs
- We have drawn one pair of parallel lines.
- We can use the same method.
- We can draw three more pairs.
- Each pair can be in a different direction.
- For example, one pair can be vertical.
- Another pair can be diagonal.
- The last pair can be in another diagonal direction.
Answer
(i) Draw a horizontal line AB. Draw a transversal CD. Choose point P on CD. Copy the corresponding angle at P to draw line JK parallel to AB. (ii) Draw a vertical line. Draw a transversal. Choose a point. Copy the corresponding angle to draw a second vertical line. (iii) Draw a diagonal line (e.g., top-left to bottom-right). Draw a transversal. Choose a point. Copy the corresponding angle to draw a second diagonal line. (iv) Draw another diagonal line (e.g., top-right to bottom-left). Draw a transversal. Choose a point. Copy the corresponding angle to draw a second diagonal line.
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