Download Geometry Inventor Files

Geometry Inventor Files
This document contains a brief description of each programme.
1. Angles in a circle
Explores the property that the angle at the centre is twice that at the
circumference
2. Angle in a semi-circle
Explores the property that when a triangle is created in a semi-circle it will
always contain a right angle
3. Angles on a straight line
Explores the fact that two angles created along a straight line add up to 180º
4. Angles on two intersecting straight lines
Explores the fact that vertically opposite angles are equal
5. Enlargement
Allows you to manipulate the original object to see what happens to the
enlargement.
6. Exploring π (Pi)
Allows you to manipulate the circle to generate a series of results recorded in
the tables. Through discussion explore the result obtained by dividing the
circumference by the diameter.
7. Exploring Trigonometry
Allows you to manipulate the diagram a number of times to generate a series
of results recorded in the tables. Using your calculator match the trigonometric
ratios to the appropriate sides of the triangle.
8. Exterior and Interior Angles of a Polygon
Use the measuring tools to measure the exterior and interior angles of the
polygon drawn – what do you notice?
9. Labelling angles – Acute and Obtuse
Use the diagram to help students to know how best to label angles.
ABC is the same as CBA
This programme has a serious shortcoming in that it can only measure angles
that are either acute or obtuse (0º – 180º) – it cannot measure reflex angles
This would also have repercussions for irregular polygons and would
impact on work completed in 8 above if you were to go on to explore
irregular polygons creating reflex interior angles.
10. Parallel Lines – Alternate
Allows you to manipulate the diagram to explore the property of alternate
angles
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11. Parallel Lines – Corresponding
Allows you to manipulate the diagram to explore the property of
corresponding angles
12. Parallel Lines – Vertically Opposite
Allows you to manipulate the diagram to explore the property of Vertically
Opposite angles
13. Polygon angle sum
The programme shows a regular octagon with angle measurements
completed on its interior angles. These have then been added to give the
angle sum. Students could then use the programme to explore angle sum for
other regular polygons
NB – if you choose to explore irregular polygons remember the programme is
unable to measure reflex angles.
14. Pythagoras Ideas
Allows you to manipulate the diagram a number of times to generate results
within the tables. Discuss what you notice about the areas of the squares.
A problem occurs when you manipulate the diagram by clicking and
holding on one of the squares. This allows you to alter the diagram in
such a way that the triangle is no-longer ‘right-angled’.
This programme may only be useful for demonstration to a class by the
teacher.
15. Reflection of a triangle
The programme demonstrates a reflection of a triangle in a mirror line. You
can manipulate the initial image and watch what happens to the reflection.
16. Tangent and Radius
Allows you to explore the relationship between the radius and tangent to a
circle
17. Tessellations using hexagons
Allows you to manipulate the hexagons to show they tessellate.
18. Tessellations using octagons
Allows you to manipulate the octagons to show they will not tessellate by
themselves. You can show that they will semi-tessellate along with a square.
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