Parallel & perpendicular
FoundationParallel never meet; perpendicular meet at 90°.
After this lesson, you can:
- Parallel lines point the same way and never meet
- Perpendicular lines meet at a right angle (90°)
- Railway rails are parallel; a plus sign is perpendicular
1Summary 重點摘要
Parallel never meet; perpendicular meet at 90°.
2Vocabulary cards Vocabulary
p
parallel lines平行線
Two lines going the same way that never meet.
p
perpendicular lines垂直線
Two lines that meet at a right angle (90°).
i
intersect相交
Two lines crossing each other.
r
right angle直角
A 90° angle, square like the corner of a book.
r
railway tracks鐵路軌
The classic parallel example: two rails that never meet.
c
cross (+ shape)十字
The classic perpendicular example: horizontal and vertical meeting at right angles.
s
set square三角尺
A triangle tool with a right angle, used to draw or check perpendicular lines.
o
opposite sides (of rectangle)長方形對邊
In a rectangle, opposite sides are parallel; neighbouring sides are perpendicular.
3Step by step Steps
- Part 1: What parallel meansParallel lines are like the two rails of a railway: they point the same way, stay the same distance apart, and never meet however far they stretch. Two lines that never meet like this are parallel, written AB ∥ DC.
- Part 2: What perpendicular meansPerpendicular lines are like a plus sign: the horizontal and vertical lines cross, and the 4 angles they make are all right angles of 90°. When two lines meet at right angles, they are perpendicular, written AB ⊥ BC.
- Part 3: How to check perpendicularityCheck with a set square. Place the right-angle corner of the set square at the point where the two lines cross. If it fits snugly with no gap, the lines are perpendicular; if there is a gap or it does not fit, they are not.
- Part 4: Find them in a rectangleParallel and perpendicular hide in rectangles. Look at a textbook: the top and bottom long edges are parallel, and each long edge meets a short edge at a right angle, so they are perpendicular. A rectangle has 2 pairs of parallel sides and 4 right angles.
- Part 5: Hunt for examplesExamples are everywhere in daily life. Parallel: a curtain rail and the ceiling, the white stripes of a zebra crossing, the two sides of lift doors. Perpendicular: the edges of a door frame, the corners of a window, a wall meeting the floor. Hunt for more around you.
- Part 6: How to draw parallel linesThere is a simple way to draw parallel lines. First draw a line with a ruler, then slide the ruler straight down 2 cm without turning it, and draw again. Do not turn the ruler as you slide; two lines with the same direction and an even gap are parallel.
4Diagrams Diagrams
5Worked example Example
Example: in rectangle ABCD, what is the relation between sides AB and BC? And between AB and DC?
- AB and BC are neighbouring sides, meeting at corner B.
- All 4 corners of a rectangle are right angles of 90°.
- So AB ⊥ BC: these two sides are perpendicular.
- AB and DC are opposite sides, pointing the same way and never meeting.
- So AB ∥ DC: these two sides are parallel.
- Answer: Answer: AB and BC are perpendicular, and AB and DC are parallel. To decide, check whether the meeting angle is a right angle for perpendicular sides; for opposite sides, the same direction with no meeting point means parallel.
6Common mistakes Mistakes
✗ Saying parallel lines only fail to meet when far apart
✓ Parallel lines never meet at any distance; same direction is the point
✗ Calling every pair of crossing lines perpendicular
✓ Perpendicular needs a right angle (90°) at the crossing
✗ Saying opposite sides of a rectangle are perpendicular
✓ Opposite sides are parallel; neighbouring sides are perpendicular
✗ Turning the ruler while drawing the second line
✓ Slide the ruler without rotating it to keep the lines parallel
7Quick check Quick check
Q1Do parallel lines ever meet?
Answer: Never
Did you get it right?
Q2At what angle do perpendicular lines meet?
Answer: 90° (a right angle)
Did you get it right?
Q3What is the relationship between railway rails?
Answer: Parallel
Did you get it right?
Q4How many pairs of parallel sides does a rectangle have?
Answer: 2 pairs
Did you get it right?
Q5How do you check perpendicularity with a set square?
Answer: Put the right angle at the crossing and see if any gap shows
Did you get it right?
8Recap Recap
- Parallel lines point the same way and never meet
- Perpendicular lines meet at a right angle (90°)
- Railway rails are parallel; a plus sign is perpendicular
- Rectangle: opposite sides parallel, neighbouring sides perpendicular
- Use a set square's right angle to check or draw perpendicular lines