Saint George Hotel 04 March 2017 MST Content Training Saint George Hotel 04 March 2017

Presentation Avhafarei Thavhanyedza Euclidean Geometry “From Policy To Practice” Presentation Avhafarei Thavhanyedza

Expected Outcomes of this training Show competency in alternative ways of handling Euclidean Geometry; Handle theorems with ease and apply them to any application problem

Approach and Methodology Applying background knowledge to shapes as foundation to Euclidean Geometry; Group discussion Facilitation Reflection Evaluation

Examiner’s reports Prove of theorems: the diagram they draw does not match the proof as the numbering of angles is incorrect. Most learners cannot reproduce theorems during examination, learners cannot lines parallel. They just state angles are alternate therefore the lines are parallel. learnt the theorem with certain letters and numbers allocated to angles but cannot apply them to a different diagram. Learners lack skills in Rider Analysis.

What could be done to address poor performance by learners? Good foundation in Euclidean Geometry. Focus more on application than proofs of theorems. Improve on teaching and learning styles; teaching methodology/ Approach; Cooperative learning styles. Instill good rider analysis skills. Make fun out of this topic; learners should play in a Maths class.

Intervention Strategies (Continues) Pay attention to converse theorems as well, as the application thereof very important as well. Learners should be taught to analyse a geometric problem, they fail to extend what is given; e.g.: if two sides of a triangle are equal then the base angles are equal. Pay attention to reasons for statements and application of the theorems. The solution of the rider usually uses the theorem proven in the previous question. Make sure the last statement before the conclusion corresponds with the reason.

Parts of the Circle

Parts of the Circle (Continues)

Definitions of concepts An Axiom: is a general statement which is accepted to be true without a proof. E.g., “Theorem of Pythagoras”. A Theorem: is a statement that can be proved by logical reasoning. A Converse: a converse uses the conclusion of a theorem to prove what is given in a theorem. A Corollary: A statement that follows a theorem which is true as a result of the theorem

Definitions of concepts Arc – a part/section of the circumference of a circle. Chord – Any straight line which touches a circle in two places. It doesn’t pass through the circle centre Diameter – a special chord passing through a centre of the circle. A diameter cuts the circle into two semi-circles. Radius – the line from the centre of the circle to any point on the circumference.

Terminologies (Continues) Secant – a line which cuts through two points on the circumference of a circle. A segment: is part of a circle cut off by a chord. Every chord cuts a circle into two segments Tangent – any line that touches the circle at one point ONLY on the circumference. Tangent is always perpendicular to the radius A Rider: the name given to a problem in Geometry

Solving Geometric Riders Draw the diagram for yourself. Split the diagram into parts that remind you of relevant theorems, i.e. Draw separated diagrams. Write down a list of properties you could use based on each diagram and each theorem. Look for links between the properties. Mark them onto the diagrams & write down the properties Look at the starting point (Given) and end points (Given and Required To Prove) and see if you can “link the links”