so that side and angle properties are easily deduced as a result of the transformation

[GeoGebra is fine for this]

for a 180 degree rotation of a triangle about the mid-point of a side:

what quadrilateral is generated?

why?

what angle and length properties follow from this transformation (rotation)?

what triangle do you need to start with to generate these quadrilaterals with a half turn about a mid-point:

- rectangle
- square
- rhombus
- 60, 120 rhombus?

for a reflection of a triangle:

what shape is created?

what angle and length properties can be deduced from the transformation (reflection)?

using a reflection, how do you create:

- an arrowhead
- a rhombus
- a square?

what angle properties exist when you reflect an isosceles triangle?

an equilateral triangle?

for trapeziums it is not so easy to see how to generate these from a transformation (an isometry)

but you can cheat a bit and use an enlargement

and the 'bit extra' is a trapezium:

what properties of the shape can you deduce from the enlargement transformation?

what extra property is there following an enlargement of an isosceles triangle?

how can a formula for the area of a trapezium be developed from the areas of the two similar triangles when the scale factor is 2 (and in general, using similar triangle ratios)?

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