Basic Geometry — Shapes & Symmetry • Topic 2 of 4

Properties of Shapes

Once a child can name shapes, the next job is to compare them by their properties — and CTET leans on four of these comparisons. First, the number of sides: a triangle has 3, a quadrilateral 4, a pentagon 5 and a hexagon 6, while a circle and an oval have none because their boundary is one unbroken curve. Second, the number of corners, or vertices, which is the point where two straight sides meet. A triangle has 3 vertices, a square and rectangle have 4, and a circle has 0 — there are no straight sides to meet. Third, the kind of boundary: circles and ovals are purely curved, polygons such as triangles and squares are purely straight, and a few shapes like the semicircle carry both. Fourth, open versus closed: a closed figure begins and ends at the same point and fences off a region (a triangle, a circle), while an open figure leaves a gap, like the letter C or a single arc. Sitting on top of all this is symmetry. A figure is symmetrical when a straight line splits it into two halves that are perfect mirror images. A square has 4 such lines, a rectangle 2, an equilateral triangle 3 and a circle infinitely many, whereas a scalene triangle — all sides and angles different — has none at all.

✅ Solved examples

1. How many sides does a pentagon have?
Five. A pentagon is a polygon with 5 straight sides and 5 vertices.
2. Why does a circle have zero vertices?
A vertex is where two straight sides meet. A circle has one continuous curved boundary with no straight sides at all, so there is nothing to form a corner — hence 0 vertices.
3. Is the printed letter 'C' an open or a closed figure?
Open. The curve of 'C' leaves a gap; its start and end points never meet, so it does not enclose a region.
4. Which one of these has both a curved and a straight boundary: circle, square, or semicircle?
The semicircle. Its arc is curved and its diameter is straight. A circle is only curved and a square is only straight.

✏️ Practice — try these, take hints as needed

1. A flat figure has 4 sides and 4 vertices. Give three shapes it could be.
Such figures are called quadrilaterals.
The angles need not all be right angles.
Any quadrilateral, e.g. square, rectangle, rhombus, parallelogram or trapezium
2. Is a scalene triangle symmetrical? Explain in one line.
In a scalene triangle all sides and all angles differ.
Could any fold line split it into matching mirror halves?
No. With all sides and angles unequal, no line divides it into two identical halves, so it has no line of symmetry
3. How many lines of symmetry does an equilateral triangle have, and where do they run?
One for each vertex.
Each line goes from a corner to the opposite side.
3 lines, each from a vertex to the midpoint of the opposite side

📝 Topic test — 8 questions

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