Properties of Angles and Lines (Including Parallel Lines)
ICSE Class 6 · Mathematics · Chapter 25
What this chapter covers
- Two lines in a plane
- Perpendicular lines
- Parallel lines
- Perpendicular bisector of a line segment
- Drawing a perpendicular to a line
Key points
- Two lines on a flat page either intersect at exactly one point or are parallel.
- The four angles formed where two lines cross add up to 360°.
- Perpendicular lines meet at a right angle, and all four angles at their meeting point are 90°. The sign is ⊥.
- Parallel lines lie in the same plane and never meet, however far they are extended. The sign is ∥.
- Parallel lines stay the same perpendicular distance apart all along their length.
- The shortest path from a point to a line is the perpendicular from the point to the line.
- The perpendicular bisector of a segment passes through its midpoint at a right angle.
- Every point on the perpendicular bisector of AB is equally far from A and B.
- With compasses and a ruler, you can draw the perpendicular bisector of a segment and a perpendicular to a line from a point on it or outside it.
Questions answered
In how many points can two different straight lines intersect?
In at most one point.
Two lines cross and one angle at the crossing is 90°. What are the other three angles?
All three are 90°, because the lines are perpendicular.
Give two examples of parallel lines from your classroom.
Possible answers: the opposite edges of the blackboard, the lines of a ruled notebook, the opposite edges of a desk top.
In the letter E, which segments are parallel and which are perpendicular?
The three bars are parallel to one another. Each bar is perpendicular to the upright stroke.
Two lines on a page are 5 cm apart at one end and 2 cm apart at the other end. Are they parallel?
No. The gap changes, so the lines will meet if they are extended.
A line segment PQ is 7 cm long. Its perpendicular bisector meets it at R. Find PR.
PR = 7 ÷ 2 = 3.5 cm.
While constructing a perpendicular bisector of AB = 6 cm, why must the compass opening be more than 3 cm?
If the opening is 3 cm or less, the arcs drawn from A and from B do not cross. There is then no point to join.
A point X is on the perpendicular bisector of CD, and XC = 4 cm. What is XD?
4 cm, because every point on the perpendicular bisector is at the same distance from both ends.