You see a shape you have never encountered before. It has 6 straight sides. How many corners does it have?
A5, because corners are one fewer than sides
B6, because in a polygon the number of corners always equals the number of sides
C7, because corners are one more than sides
DYou cannot tell without seeing the shape
In any shape made entirely of straight sides, every pair of adjacent sides meets at exactly one corner — so the number of corners always equals the number of sides. You don't need to see the shape; the property tells you the answer. This is the power of properties: they let you reason about shapes you've never met before.
Question 2 Multiple Choice
Which of these correctly describes what makes a circle different from all polygon shapes?
AA circle has more sides than any polygon
BA circle has no straight sides and no corners
CA circle's sides are curved instead of straight
DA circle is smaller than most polygons
A circle has zero sides and zero corners — its boundary is one continuous curve with no straight sections and no points where two sides meet. Option C is tempting but inaccurate: a circle doesn't have 'curved sides' because it has no sides at all. The absence of sides and corners is the defining property of a circle.
Question 3 True / False
In any shape made entirely of straight sides, the number of sides always equals the number of corners.
TTrue
FFalse
Answer: True
This is always true for polygons. Each side connects to the next at a corner, so each side contributes exactly one corner. A triangle has 3 sides and 3 corners; a square has 4 and 4; a hexagon has 6 and 6. The pattern never breaks for shapes with straight sides.
Question 4 True / False
A tall, narrow rectangle and a short, wide rectangle are different shapes because they look different.
TTrue
FFalse
Answer: False
Both are rectangles because both have 4 sides and 4 corners — the same property list. Shapes are defined by their properties, not by their proportions, size, or orientation. This is the core insight: two shapes that look quite different can be the same kind of shape if they share the same properties.
Question 5 Short Answer
A friend says she knows a shape is a square because it 'has four sides that all look the same.' What is right about her reasoning, and what would make it even stronger?
Think about your answer, then reveal below.
Model answer: She is right to use side count and equal side length as properties. To make it stronger, she could also check that it has exactly 4 corners. Describing properties precisely (counting sides, checking corners) is more reliable than judging by appearance alone, since two shapes can look similar but have different properties.
Relying on visual appearance alone can lead to mistakes — a diamond (rotated square) might not 'look like' a square, but it has the same properties. Building the habit of checking side and corner counts rather than just eyeballing a shape is the key shift that makes geometry reasoning reliable.