Classifying Shapes: Step-by-Step Guide
We sort shapes into groups by their properties: how many sides they have, whether the sides are equal, what kinds of angles they have, and whether sides are parallel. Triangles are named by their sides (scalene, isosceles, equilateral) and by their angles (acute, right, obtuse). Four-sided shapes fit into a family tree, from trapezoids to parallelograms to rectangles and rhombuses to squares.
Math Racer skill guide · Elementary · Grades K-5
How to solve it, step by step
- Count the sides. 3 sides is a triangle, 4 is a quadrilateral, 5 is a pentagon, 6 is a hexagon, and so on.\[n = \text{number of sides}\]
- Look at the side lengths. Triangles: all sides equal is equilateral, two sides equal is isosceles, no sides equal is scalene. Four-sided shapes: opposite sides equal might be a parallelogram, and all four sides equal might be a rhombus or a square.\[\text{equilateral},\;\text{isosceles},\;\text{scalene}\]
- Look at the angles. Triangles: all angles smaller than 90 degrees is acute, one 90 degree angle is right, one angle bigger than 90 degrees is obtuse. Four-sided shapes: four right angles means a rectangle, or a square if the sides are equal too.\[\text{acute},\;\text{right (90}^\circ\text{)},\;\text{obtuse}\]
- Check for parallel sides. Four-sided shapes: no parallel sides is just a quadrilateral, one pair is a trapezoid, and two pairs make a parallelogram.\[\text{trapezoid: 1 pair }\parallel,\;\text{parallelogram: 2 pairs }\parallel\]
- Pick the most specific name. Use the best name that fits. A square is also a rectangle, but we call it a square because that tells us the most.\[\text{square} \subset \text{rectangle} \subset \text{parallelogram} \subset \text{quadrilateral}\]
Worked example
A quadrilateral has four sides of equal length and four right angles. Classify it as specifically as possible.
Step 1: Count the sides: 4 sides, so it is a quadrilateral.
Step 2: Look at the sides: all four are equal, so it could be a rhombus.
Step 3: Look at the angles: all four are 90 degrees, so it could be a rectangle.
Step 4: Check for parallel sides: both pairs of opposite sides are parallel, so it is a parallelogram too.
Step 5: It has all sides equal (like a rhombus) and all right angles (like a rectangle). A shape like that is a square.
The most specific name is: square.
Tips and common mistakes
- Use the most specific name. A square is also a rectangle, a rhombus, a parallelogram, and a quadrilateral, but 'square' tells you the most.
- A triangle can have two names: one for its sides and one for its angles, like 'isosceles right triangle'.
- An equilateral triangle has all three angles equal to 60 degrees.
- A trapezoid has at least one pair of parallel sides. Some books say exactly one pair, so check which one your class uses.
- A rhombus has four equal sides. A rectangle has four right angles. A square has both.
- When you draw a shape, use small tick marks on equal sides and small arcs on equal angles.
- A regular polygon has all its sides equal and all its angles equal.
- A kite has two pairs of equal sides that are next to each other. A rhombus has all four sides equal. Do not mix them up.