1. Properties of Geometrical Figures
Stage 4
Geometry
9/22/2018

2. Properties of Geometrical Figures
Main points covered in this unit:
Classify triangles by angles or sides
Distinguish between convex and non convex figures
Investigate special quadrilaterals with respect to sides, angles, diagonals, symmetry
Investigate line and rotational symmetry
Use the angle sum of a triangle or quadrilateral to find missing angles or sides.
Geometry
9/22/2018

3. Properties of Geometrical Figures Vocabulary
triangle scalene isosceles equilateral angle side properties diagonal quadrilateral symmetry rotational line kite trapezium rectangle square rhombus parallelogram convex non-convex polygon perpendicular parallel acute right obtuse reasoning
book
Geometry

4. Two Ways to Classify Triangles
By Their Sides
By Their Angles
Geometry
9/22/2018

5. Classifying Triangles Scalene Triangles
No sides are the same length, all angles are different to each other
book
Geometry
9/22/2018

6. Isosceles Triangles
Two sides are the same length, and the two base angles are equal
book
Geometry
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7. Equilateral Triangles
Three sides are the same length, all angles are equal (600)
book
Geometry
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8. Classifying Triangles By Their Angles
Acute
Right
Obtuse
Geometry
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9. Classifying Triangles By Their Angles
Acute
Right
Obtuse
Geometry
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10. Acute Triangles Acute triangles have three acute angles book Geometry
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11. Right Triangles Right triangles have one right angle book Geometry
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12. Obtuse Triangles Obtuse triangles have one obtuse angle book Geometry
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13. Classify this triangle.
Right Scalene
Geometry
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14. Classify this triangle.
Obtuse Isosceles
Geometry
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15. Classify this triangle.
Acute Scalene
Geometry
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16. Classify this triangle.
Acute Isosceles
Geometry
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17. Classify this triangle.
Obtuse Scalene
Geometry
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18. Classify this triangle.
Right Isosceles
Geometry
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19. Geometry
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20. Geometry
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21. Polygons
A polygon is a closed plane figure with straight sides which do not cross each other. We further classify polygons as either convex (no interior reflex angles) or non-convex ( at least one interior angle which is reflex)
convex
polygon
book
non-convex
polygon
A regular polygon is one which has all equal sides and angles.
Geometry
9/22/2018

22. Copy the table into your book. Complete the columns
with ticks or crosses.
book
Geometry
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23. Geometry
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24. Geometry
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25. Explain this diagram using words:
Geometry
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26. Quadrilaterals
In groups, discuss the following quadrilaterals (4 sided shapes) focusing on each of the following:
Sides (opposite and adjacent)
Angles
Diagonals and whether they are equal, bisect and the angles they meet at
The shapes are: square, rectangle, trapezium, kite, parallelogram and rhombus.
You will report back to the class…so work carefully!
Geometry
9/22/2018

27. Always, Sometimes, Never
A parallelogram is _______ a quadrilateral
A trapezium is _______ a kite
A kite is _______ a rectangle
A quadrilateral is _______ a square
A square is _______ a rectangle
A quadrilateral is _______ a rectangle
A parallelogram is _______ a kite
A square is _______ a quadrilateral
A trapezium _______ has five sides
A quadrilateral _______ has opposite sides parallel
A square is _______ a rhombus
A rhombus is _______ a square
Geometry
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28. Geometry
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29. Geometry
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30. Symmetry Symmetry can be either reflectional or rotational.
Reflectional symmetry means the image has at least one axis of symmetry ( a line which acts as a mirror, so both halves of the image are identical but reflections of each other). This axis of symmetry can be horizontal, vertical, or neither.
Rotational symmetry means that when an object is rotated, at least once in a full rotation it will look exactly the same as the original image. The order of rotational symmetry is how many times in a revolution the shape looks exactly the same.
book
Geometry
9/22/2018

31. Discuss each of these with respect to symmetry
Geometry
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32. Geometry
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33. Geometry
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34. A shape has exactly one axis of symmetry. What could it be?
A shape only has one KIND of symmetry.
Create a ‘non-standard’ plane shape which has rotational
symmetry.
A plane shape has six sides and two 900 angles.
What could it look like?
A shape has some pairs of perpendicular lines and some pairs
of parallel sides. What could it look like?
Create two shapes with different names that each have two pairs
of equal sides. How are they alike? How are they different?
Problem solving
Geometry
9/22/2018

35. Sketch what it says:
Geometry
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36. Make 5 comments about the Mathematics you can see in this image
Make 5 comments about the Mathematics you can see in this image. Create a similar image using a different combination of shapes.
Geometry
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37. Angle Sum of Triangle
Geometry
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38. Angle Sum of a Triangle The angles in any triangle add to 1800.
Construct a proof:
book
Geometry
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39. Geometry
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40. Geometry
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41. Geometry
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42. 9
Geometry
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43. Angle Sum of a Quadrilateral
Geometry
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44. Angle Sum of a Quadrilateral
In any quadrilateral, the angles add to 3600.
Construct a proof:
book
Geometry
9/22/2018

45. Geometry
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46. Geometry
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47. Super Challenge Questions…
Geometry
9/22/2018