AS+1.6+Geometric+Reasoning

Back to year 11 page 1.6 Geometric Reasoning Achievement Standard

The main content for this topic is:
 * Pythagoras
 * Trigonometry (in right-angled triangles)
 * Similar Triangles
 * Angles in Parallel Lines and at Intersections
 * Angles in Polygons
 * Angles in Circles

The content for all the levels of achievement is the same. The tasks that can extract Excellence grades are multi-step and require good clear communication, step by step working, as well as some insight. Usually if the logic is missing in the argument or the context isn't taken into account, then the grade assessed is lower.

The assessment is based on Bloom's Taxonomy. Achievement is reading what is on the lines (eg find missing angle A), Merit is reading between the lines (finding a connection between a few missing angles) and Excellence is beyond the lines. Have a look at this symbolic representation of the related thinking etc - called Solo Taxonomy.

= PYTHAGORAS =

**Pythagoras**: Here's a cute little interactive exercise which can be thought of as a "proof" of Pythagoras. Click on the image below. Have some fun.



And a cute little "proof" :


**Geogebra** link: Geogebra is a free program to use. Here's a little demo of **Pythagoras**. Just move point A, B or C and watch the areas change. The areas of the two smaller squares add up to the area of the biggest square (on the longest side, the hypotenuse). media type="custom" key="25371076" align="left" width="40" height="40"

= TRIGONOMETRY =

**Geogebra** link: Here's a right-angled triangle with one angle fixed at 30 degrees. Move point A to change the size of the triangle and look to see if there are any changes in the ratios of the side lengths. This topic is called ** Trigonometry. **

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Click for some notes that might help you in the early stages of working out the length of a missing side.

The is a simple method that always works with Trig. Have a look at this. The notes are for finding the length of a missing side but they are useful for finding missing angles too. For finding angles you must remember the last step of "Shift Cos" or "Shift Sin" or "Shift Tan" otherwise known as Cos -1 etc.

= ANGLES =

**Exterior Angles** always add up to 360 degrees. Have a look at this Geogebra widget. You can alter the size of the polygon (quadrilateral in this case) and change the angle sizes by moving the red dot.

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Make the shape really small and it becomes obvious that the Exterior Angles add up to 360 degrees.