32
Parallel and perpendicular lines
Textbook: Part 1, lesson 32, pp. 126–127
GoalDistinguish parallel and perpendicular lines; find the angles formed by intersecting lines.
New words
parallel · parallelperpendicular · perpendikulyarvertical angles · vertikal burchaklarpoint of intersection · kesishish nuqtasi
Explanation
Two lines that do not intersect are called parallel, written a ∥ b; for example, opposite sides of a rectangle are parallel. When two lines intersect, four angles are formed; angles opposite each other are vertical angles and are equal. Two neighbouring angles on one straight line add up to 180°, and all four angles add up to 360°. Lines that intersect at a right angle (90°) are called perpendicular, written a ⊥ b. When perpendicular lines intersect, four right angles are formed.
Worked examples
If one angle formed by two intersecting lines is 50°, its vertical angle is also 50° and the other two are 180° − 50° = 130° each. Check: 50 + 130 + 50 + 130 = 360.
The horizontal lines in a squared notebook are parallel to each other, and the vertical lines are perpendicular to the horizontals: they meet at 90°.
Class activity
“Lines in the classroom”: pupils find parallel and perpendicular segments in the room (window frame, desk edges) and note them as a ∥ b or a ⊥ b.
Practice
1
Two lines intersect and one angle is 65°. How many degrees is its vertical angle?
65
2
How many degrees is the neighbouring angle that forms a straight line with the 65° angle?
115
3
The angles of two intersecting lines are 50°, 130°, 50°, 130°. What is their sum?
360
4
Why are all four angles 90° when perpendicular lines intersect?
One angle is 90°; its vertical angle is 90° too and the neighbours are 180° − 90° = 90°.