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

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

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

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

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

Isosceles Triangles Two sides are the same length, and the two base angles are equal book Geometry 9/22/2018

Equilateral Triangles Three sides are the same length, all angles are equal (600) book Geometry 9/22/2018

Classifying Triangles By Their Angles Acute Right Obtuse Geometry 9/22/2018

Classifying Triangles By Their Angles Acute Right Obtuse Geometry 9/22/2018

Acute Triangles Acute triangles have three acute angles book Geometry 9/22/2018

Right Triangles Right triangles have one right angle book Geometry 9/22/2018

Obtuse Triangles Obtuse triangles have one obtuse angle book Geometry 9/22/2018

Classify this triangle. Right Scalene Geometry 9/22/2018

Classify this triangle. Obtuse Isosceles Geometry 9/22/2018

Classify this triangle. Acute Scalene Geometry 9/22/2018

Classify this triangle. Acute Isosceles Geometry 9/22/2018

Classify this triangle. Obtuse Scalene Geometry 9/22/2018

Classify this triangle. Right Isosceles http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#triangles Geometry 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

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. http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#triangles Geometry 9/22/2018

Copy the table into your book. Complete the columns with ticks or crosses. book Geometry 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

Explain this diagram using words: Geometry 9/22/2018

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! http://teams.lacoe.edu/documentation/classrooms/amy/geometry/6-8/activities/quad_quest/quad_quest.html Geometry 9/22/2018

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 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

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. https://hwb.wales.gov.uk/cms/hwbcontent/Shared%20Documents/vtc/ngfl/maths/greg_morgan_symmetry/index.htm book Geometry 9/22/2018

Discuss each of these with respect to symmetry Geometry 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

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

Sketch what it says: Geometry 9/22/2018

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 9/22/2018

Angle Sum of Triangle Geometry 9/22/2018

Angle Sum of a Triangle The angles in any triangle add to 1800. Construct a proof: book Geometry 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

9 Geometry 9/22/2018

Angle Sum of a Quadrilateral Geometry 9/22/2018

Angle Sum of a Quadrilateral In any quadrilateral, the angles add to 3600. Construct a proof: book Geometry 9/22/2018

Geometry 9/22/2018

Geometry 9/22/2018

Super Challenge Questions… Geometry 9/22/2018