P3 Parallel and Perpendicular Lines
How a set-square corner identifies perpendicular lines and how matching directions identify parallel lines, even when both drawings are tilted.
⏱ 7 min · 🎯 3 things to master
Lines do not need to be horizontal or vertical to have a special relationship. Two tilted lines can cross like a set-square corner, or they can keep the same direction and never meet when extended.
Parents: give your child a ruler and set square. Ask them to predict the relationship from the tools before they tap a tilted example in the lab.
By the end you will be able to recognise and draw perpendicular and parallel lines, including finite segments whose extensions do not meet.
Perpendicular lines meet at a square corner
cross at a right angle. A set square lets you check the corner without measuring a number. In the tilted example, labelled AB and CD cross at P, where the marked corner is square.
🤔 Predict first: Two tilted lines meet at a set-square corner. What are they?
Line relationship lab
Predict first: Two lines keep the same direction and never meet when extended. What are they?
Parallel lines keep the same direction
have matching directions. The finite segments may stop before they meet, so imagine extending both. In the tilted example, labelled AB and CD point the same way. Their dashed extensions never meet.
The little matching arrows are a visual clue. A ruler keeps each segment straight. A set square can move along the ruler to copy the direction through another point.
🤔 Predict first: Two finite tilted segments point in the same direction. What happens when they are extended?
Draw with a ruler and set square
To draw a perpendicular through P on AB, place one edge of the set square along AB and draw along the other edge through P. The resulting line meets AB at a square corner. To draw a parallel through C, keep the ruler as a guide, move the set square without turning it, and draw the copied direction through C.
- 1. PlaceSet-square edge follows AB at P.
- 2. DrawTrace the other edge through P.
- 3. CheckThe crossing has a square corner.
- 1. PlacePut the set-square edge along AB at Q; rest the ruler against its other edge.
- 2. SlideKeep the ruler fixed; slide the set square to C.
- 3. DrawTrace the copied direction through C.
The lab above shows the same baseline, labelled point and tool actions as a hands-on check.
🤔 Predict first: To copy AB through C as a parallel, should you turn the set square or move it without turning?
Three construction practice checks
Use the labelled diagrams and decide which tool action you would make before opening each solution.
Practice 1 — classify a crossing
The labelled lines AB and CD cross at P. A set-square marker is at the crossing. What is the relationship?
Show the worked classification
Check the square corner
The lines are perpendicular.
Practice 2 — classify finite segments
The labelled finite segments AB and CD have matching direction arrows. What is the relationship when extended?
Show the worked classification
Copy the direction
The segments represent parallel lines.
Practice 3 — draw through a point
AB is the baseline and P is the labelled point on AB. Use a ruler and set square to draw through P at a square corner. What should the relationship be?
Show the construction check
Use the set-square corner
The new line is perpendicular to AB.
Watch out — these are easily mixed up
Quick recap
🎯 Mastery check
Answer all 8 — your progress is saved on this device.
Two lines meet at a set-square corner. What are they?
Two finite segments keep the same direction when extended. What are they?
Which tool draws a straight line segment?
Which tool checks the square corner where two lines cross?
AB and CD have matching direction arrows, and they do not meet when extended. What is CD to AB?
To copy AB as a parallel through C, what should happen to the set square?
A line through P uses a set-square corner to cross AB. What relation should you name?
Can tilted lines be parallel?