Polygons
What is a polygon?
A polygon is a closed shape with three or more straight sides. None of the sides cross over each other.
Draw an equilateral triangle
All three sides and angles the same size.
The interior angles in a quadrilateral should equal what?
360 degrees
Name four ways that you could classify a shape
Length of sides
Number of sides
Number of angles
Size of angles
Parallel sides
Right angles
Give one example each of a regular and an irregular quadrilateral.
Regular: Square
Irregular: Rectangle, Rhombus, Parallelogram, Trapezium
What is an irregular vs a regular polygon?
A regular polygon has all of its sides and angles the same. An irregular polygon has different sides and angles.
(No sides are the same length, no angles are equal)
The interior angles in a triangle should equal what?
180 degrees
Two quadrilaterals both have:
Explain why this information alone is not sufficient to classify either shape.
You also need information about side lengths, angle sizes, or parallel sides.
What is a trapezium? Draw one and be ready to describe it.
A trapezium is a 2D quadrilateral shape with at least one pair of opposite sides that are parallel. It has four sides, four vertices, and its internal angles always sum up to 360 degrees.
What is a quadrilateral polygon?
A quadrilateral polygon is a shape with four straight sides, four vertices (corners) and four internal angles that add up to 360 degrees.
A triangle is classified by its internal angles and the length of the three sides.
How can you figure out the measurement of one unknown angle within a triangle, if you are given the other two?
Subtract the two known angles from 180 (the total sum of all angles in a triangle). The resulting number will be the final angle.
Explain why a square is considered a special type of rectangle, but a rectangle is not always a square.
A square meets all rectangle properties (four right angles, opposite sides parallel). A rectangle does NOT meet all square properties - namely it does not have four equal sides.
Describe the similarities and differences between a trapezium and a parallelogram.
A parallelogram and a trapezium are both quadrilaterals with 4 sides and 360 degree internal angles. The main difference is that a parallelogram has two pairs of parallel opposite sides, whereas a trapezium has only one pair.
Give an example of an irregular polygon
Irregular polygons are polygons that do not have equal sides and equal angles. Common examples of irregular polygons are a scalene triangle, kite, rectangle.
Name and describe four different types of triangle.
Scalene Triangle: No sides are the same length, no angles are equal.
Right-angle: There is a right angle (90 deg) in the triangle.
Isosceles Triangle: Two sides are the same length, two angles are the same.
Equilateral triangle: All sides are the same length, all angles are the same.
Find the three internal angles of an equilateral triangle.
60 degrees each. Equilateral triangles have three equal angles, therefore 180 divided by 3 = 60
A shape fits all of these rules:
Why can it never be a rectangle or parallelogram?
Rectangles and parallelograms require two pairs of parallel sides.
A quadrilateral has four equal sides but no right angles.
Name the quadrilateral it must be and explain why.
Rhombus — all sides are equal, but angles are not 90°.
Name at least 12 different polygons
Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon (11 sides), Dodecagon (12 sides), Icosagon (20 sides), Regular/Irregular Polygon, Equilateral Polygon,
Quadrilaterals:
Square, rectangle, rhombus, parallelogram, trapezium
Note: Circles and ovals are 2D shapes but are NOT considered polygons because they have curved sides, not straight line segments.
What is the size of the two acute angles in an isosceles right-angled triangle?
Right angle = 90 degrees.
Isosceles = two angles the same.
So: 180-90 = 90.
90 divided by 2 = 45
45 degrees
Explain the properties of a rhombus?
A rhombus is a quadrilateral with four equal sides. Opposite angles are equal to each other, with two angles being acute and two angles being obtuse.
Draw a quadrilateral with:
Explain why the shape cannot be a square or rectangle, and name what it could be.
Cannot be square or rectangle because both require four right angles. It could be a rhombus.
Which quadrilaterals always have two pairs of parallel sides?
Name all that apply and justify one of your choices.
Parallelogram, rectangle, rhombus, square.
(Justification example: “A rectangle has opposite sides parallel by definition.”)