Question 1: Plot two parallel lines, each 4 cm apart, on the grid. Label them as line AB and line CD. Confirm they are parallel.

Answer: Lines AB and CD are equidistant and do not intersect.

Question 2: Calculate the distance between two parallel lines if the perpendicular segment between them measures 6 cm.

Answer: 6 cm

Question 3: Construct a line segment that is 5 cm from a given line, ensuring it is parallel to the original line.

Answer: A line parallel and 5 cm away from the original line.

Question 4: Explain why a line parallel to a transversal cuts two lines at equal angles.

Answer: Because corresponding angles are equal when lines are parallel, and a line parallel to the transversal preserves these angle properties.

Question 5: Given two parallel lines and a transversal, find the measure of an alternate interior angle if the corresponding angle is 65°.

Answer: 65°

Question 6: A road runs parallel to a railway track 3 km away. If a person walks perpendicular from the road to a point 4 km along the railway, how far is the person from the starting point? (Assume straight paths).

Answer: Use Pythagoras: √(3² + 4²) = 5 km

Question 7: Construct a pair of parallel lines and a transversal such that one of the alternate interior angles is 120°. Label all relevant angles.

Answer: Angles alternate interior: 120°, corresponding: 120°, and alternate exterior angles also 120°.

Question 8: A train track runs parallel to a river 2 km away. A boat crosses the river from one bank directly to a point 1 km downstream on the opposite bank. How far downstream from the starting point does the boat land?

Answer: Use Pythagoras: √(2² + 1²) = √5 km

Question 9: Identify and correct the mistake: A student draws two lines that look parallel but are not equidistant at all points. What is the common error?

Answer: The student did not ensure the lines are drawn with a constant perpendicular distance; they are not truly parallel.

Question 10: Challenge: Prove that the locus of points equidistant from two parallel lines forms two lines parallel to the original lines.

Answer: Locus lines are parallel to the original lines, each at a fixed perpendicular distance, forming two lines equidistant from the originals.

Question 11: A diagram shows two parallel roads and a perpendicular crossing path. If the roads are 3 km apart, and the crossing is 4 km long, what is the total distance covered if someone walks along the crossing and then along one road?

Answer: Total distance = 4 km + 3 km = 7 km.