Consider Each Statement in Turn and Decide Whether the Statement Is Always True, Sometimes
Consider each statement in turn and decide whether the statement is always true, sometimes true or never true. All members of the group must explain their thinking and all members of the group must agree the decision.
1. A rhombus could also be called a squareSometimes / 2. An isosceles triangle contains a reflex angle
Never
3. All pyramids have an even number of edges
Always / 4. Shapes with the same perimeter have the same area
Sometimes
5. The number or straight edges in any prism is a multiple of 3
Always / 6. The number of lines of symmetry for a regular polygon is equal to the number of sides
Always
1. Properties of a rhombus are:-
Opposite sides equal and parallel
Opposite angles equal
Two lines of symmetry
Properties of a square are:-
Opposite sides equal and parallel
Opposite angles equal
Four lines of symmetry
Therefore a square is a special sort of rhombus.
2. The sum of the angles in any triangle is 180˚
Therefore one angle could not be 180˚ as this would give a straight line.
NB: sometimes the question is interpreted in a different way. Colleagues may suggest that the answer is always because the external angle of a triangle will be bigger than 180. This is an area for further discussion in your group, in terms of how to use ambiguous questions to develop conflict discussion in mathematics. See Ryan and Williams (main article).
3. All pyramids have an even number of edges. There will be double the number of edges as the number of edges around the base because a straight line (an edge) joins each vertex to the apex.
4. E.g.
5. Because a prism is a polyhedron consisting of two opposite identical faces with their vertices joined by parallel lines the number of edges must be a multiple of 3. eg triangular prism triangle 1 has 3 edges, triangle 2 has 3 edges. They are joined by three oblongs and the edges of the oblongs join the triangles at either end. A good time to point out that a cylinder in not a prism because it is not joined by straight edges, but by a single curved surface.
6. Because regular polygons have sides that are equal length and angles that are all equal in size it follows that all angles can be bisected to form lines of symmetry. This notion that one property precedes or follows from another, and can therefore deduce one property from another is discussed in the article that is the feature of today’s session.
It may be worthwhile also spending some time discussing the properties of a circle.
A circle does not have one side (as often mis-represented) in many published schemes. Some mathematicians like to think of a circle as a regular polygon with an infinite number of sides.
Circle is a 2d shape consisting of all the points that are a given distance from a fixed point called the centre of a circle.