97
Perpendicular lines
Textbook: Part 3, lesson 97, pp. 89–91
GoalPerpendicular lines: they meet at a right angle; drawing a perpendicular.
New words
perpendicular · perpendikularright angle · to‘g‘ri burchakpoint of intersection · kesishish nuqtasiset square / angle ruler · burchak o‘lchagich
Explanation
If two straight lines meet at a right angle, they are called perpendicular. We write a ⊥ b. If we fold a sheet of paper twice and open it, the fold lines are perpendicular. Neighbouring lines of a notebook grid are perpendicular too, as are adjacent sides of a rectangle or a square. To draw a perpendicular we place the right angle of a set square against the line. Parallel lines never meet; perpendicular lines meet at a right angle.
Worked examples
At each vertex of a square two adjacent sides are perpendicular. A square has 4 vertices, so it has 4 pairs of perpendicular sides.
For a segment AB = 10 cm the midpoint O gives AO = 10 : 2 = 5 cm. To draw the perpendicular through O we put the set square at O.
Class activity
“Fold and check”: children fold a sheet twice, check the angle between the fold lines with a set square and count the 4 right angles formed.
Practice
1
How many pairs of perpendicular (adjacent) sides does a square have?
4
2
What is the perimeter in centimetres of a rectangle with sides 4 cm and 7 cm?
22
3
A sheet of paper is folded twice and opened. How many right angles are formed where the fold lines cross?
4
4
The midpoint of segment AB = 10 cm is O. How many centimetres is AO?
5
5
At which time are the hour and minute hands perpendicular: 3:00 or 12:00?
3:00