Basic Geometry — Shapes & Symmetry • Topic 1 of 4

Plane Shapes (2-D Shapes)

A plane shape is flat. It has length and breadth but no thickness, which is why we also call these two-dimensional or 2-D figures. The first cut a child learns is curved versus straight. A circle is a closed curved shape where every point on the boundary sits the same distance from the centre. A semicircle is exactly half of that circle, so it carries one straight edge (the diameter) and one curved edge (the arc). An oval is the egg-like, stretched cousin of the circle — curved all the way round, but not perfectly round. On the straight-sided team you have the polygons: closed figures built only from straight line segments. The smallest possible polygon is the triangle, with 3 sides, 3 corners and angles that always add up to 180 degrees. The square has 4 equal sides and four right angles; the rectangle keeps the four right angles but only its opposite sides match in length. For the exam, the skill being tested is recognition — pick the shape out of a tap, a window, a slice of pizza, a coin — plus the counting of sides, vertices and the odd diagonal, and the habit of asking first whether a boundary is curved or straight.

✅ Solved examples

1. How many vertices (corners) does a triangle have?
Three. A triangle is the smallest polygon, with 3 straight sides meeting at 3 vertices.
2. A square sheet of paper is folded exactly in half, edge to edge. What shape do you get?
A rectangle. Halving a square edge-to-edge keeps the four right angles but makes one pair of sides shorter, so the result is a rectangle (not a square).
3. A child draws a closed figure with no straight lines and no corners, but it is not perfectly round like a coin — it looks like an egg. Name it.
An oval. It is curved throughout, like a circle, but stretched, so it is neither a polygon nor a true circle.
4. How many straight edges and how many curved edges does a semicircle have?
One of each. The straight edge is the diameter and the curved edge is the arc, so a semicircle mixes both kinds of boundary.

✏️ Practice — try these, take hints as needed

1. What is the least number of straight line segments needed to make a closed polygon?
Two segments cannot close up into a region.
Think of the simplest polygon.
Three (they form a triangle)
2. Name the one property that is true for every square but not for a general rectangle.
Both have four right angles, so it is not about the angles.
Compare the side lengths.
All four sides are equal in a square; a rectangle has only its opposite sides equal
3. A classroom blackboard has opposite sides equal and four right angles. Which shape is it?
Four right angles rules out a triangle and a circle.
Only the opposite sides match, not all four.
Rectangle

📝 Topic test — 8 questions

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