Lines, Angles, Symmetry
Lines, Angles, Symmetry
A line has no end points, a ray has one, and a line segment has two. Angles are measured in degrees and named by size. Symmetry means one half of a figure is the mirror image of the other. All three are Class 3-5 content and all three appear in CTET.
Lines
- Line — extends endlessly in both directions.
- Line segment — has two end points and a fixed length.
- Ray — has one end point and extends endlessly in one direction.
- Parallel lines — always the same distance apart, never meet.
- Intersecting lines — meet at one point.
- Perpendicular lines — intersect at 90 degrees.
Angles by size
| Angle | Measure |
|---|---|
| Acute | More than 0 and less than 90 degrees |
| Right | Exactly 90 degrees |
| Obtuse | More than 90 and less than 180 degrees |
| Straight | Exactly 180 degrees |
| Reflex | More than 180 and less than 360 degrees |
| Complete | Exactly 360 degrees |
Two angles are complementary if they add to 90 degrees and supplementary if they add to 180 degrees. The letters help: C comes before S, and 90 comes before 180.
Symmetry
- Line symmetry — a figure can be folded so the two halves match exactly. A square has 4 lines of symmetry, a rectangle 2, an equilateral triangle 3, a circle infinitely many, and a scalene triangle none.
- Rotational symmetry — the figure looks the same after a partial turn. A square has rotational symmetry of order 4.
- Letters with vertical symmetry: A, H, I, M, O, T, U, V, W, X, Y. With horizontal symmetry: B, C, D, E, H, I, K, O, X.
Angles around a point and on a line
Three facts settle most angle questions at this level. Angles on a straight line add to 180 degrees. Angles around a point add to 360 degrees. When two lines cross, the vertically opposite angles are equal. A Class 5 child can find an unknown angle in almost any simple figure with these three alone, without any formula.
The Class 3-5 way in
Symmetry is taught with paper folding, ink blots, cut-outs and rangoli patterns before any definition is given. Children fold a paper, cut a shape and open it — the fold line is the line of symmetry, discovered rather than told.
✗ A rectangle has 4 lines of symmetry like a square. | ✓ A rectangle has only 2; the diagonals of a rectangle are not lines of symmetry.
संकेत: पूरक कोण (complementary) = योग 90 डिग्री; संपूरक कोण (supplementary) = योग 180 डिग्री।
Expect one to two questions. The most repeated is the number of lines of symmetry in a common figure, and the rectangle is the usual trap because candidates count the diagonals. The complementary-supplementary pair is asked directly almost every cycle. Also learn the letter symmetry lists, since a question sometimes asks which capital letter has a horizontal line of symmetry.
Frequently asked questions
What is the difference between complementary and supplementary angles?
Two angles are complementary when their measures add up to 90 degrees, and supplementary when they add up to 180 degrees. Remembering that C comes before S, as 90 comes before 180, prevents the usual confusion.
How many lines of symmetry does a rectangle have?
Two — one horizontal and one vertical through the midpoints of opposite sides. The diagonals of a rectangle are not lines of symmetry, although the diagonals of a square are, which is why a square has four.
What is the difference between a line, a ray and a line segment?
A line extends endlessly in both directions, a ray has one fixed end point and extends endlessly in the other direction, and a line segment has two end points and therefore a definite measurable length.
60-second recap
- Line has no ends, ray has one, segment has two.
- Acute under 90, right 90, obtuse 90 to 180, straight 180, reflex 180 to 360.
- Complementary add to 90; supplementary add to 180.
- Lines of symmetry: square 4, rectangle 2, equilateral triangle 3, circle infinite.
- Teach symmetry by folding and cutting before defining it.