Understanding Elementary Shapes
Classifying Triangles
Triangles are named by their sides: scalene (no equal sides), isosceles (2 equal sides) and equilateral (3 equal sides). They are also named by their angles: acute (all angles < 90°), right (one 90° angle) and obtuse (one angle > 90°).
Example 1: What do we call a triangle with a 90° angle?
A right triangle.
Example 2: What do we call a triangle with all sides equal?
An equilateral triangle.
Quick recap
- By sides: scalene, isosceles, equilateral.
- By angles: acute, right, obtuse.
✓ Quick check
A triangle with all angles less than 90° is ___ ?
All angles under 90° make an acute triangle.
A triangle with exactly 2 equal sides is ___ ?
Two equal sides make an isosceles triangle.
Quadrilaterals & Polygons
Quadrilaterals have 4 sides: square, rectangle, rhombus, parallelogram and trapezium (exactly one pair of parallel sides). A polygon is a closed shape with straight sides; a pentagon has 5 sides and a hexagon has 6. A regular polygon has all sides and angles equal.
Example 1: What is a polygon with 5 sides called?
A pentagon.
Example 2: Which quadrilateral has exactly one pair of parallel sides?
A trapezium.
Quick recap
- Quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium.
- Pentagon = 5 sides; hexagon = 6 sides; regular = all sides/angles equal.
✓ Quick check
How many sides does a hexagon have?
A hexagon has 6 sides.
A quadrilateral with all sides equal and 4 right angles is a ___ ?
Equal sides plus right angles make a square.
3D Shapes: Faces, Edges & Vertices
Solid (3D) shapes have faces (flat surfaces), edges (where faces meet) and vertices (corners). A cube has 6 faces, 12 edges and 8 vertices. A cone has 2 faces, 1 edge and 1 vertex, while a sphere has 1 curved face, 0 edges and 0 vertices.
Example 1: How many faces does a cube have?
6 faces.
Example 2: How many vertices does a cone have?
1 vertex (the apex).
Quick recap
- Cube/cuboid: 6 faces, 12 edges, 8 vertices.
- Cone: 2 faces, 1 edge, 1 vertex; sphere: 1 face, 0 edges, 0 vertices.
✓ Quick check
How many edges does a cuboid have?
A cuboid has 12 edges.
How many vertices does a sphere have?
A sphere has no vertices.
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