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### NT Year 11 – 13: Planar Geometry Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Year 11 – 13: Planar Geometry
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
3 Geometry-angles Complementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
4 Geometry-angles Vertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
5 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
6 Geometry-problems Additional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
7 2-D shapes Recognise and name triangles
Objective: On completion of the lesson the student will be able to recognise and correctly name triangles according to their properties.
8 Special triangles Special triangles
Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.
9 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
10 Geometry-congruence Congruent triangles, Test 1 and 2
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent.
11 Geometry-congruence Congruent triangles, Test 3 and 4
Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.
12 Geometry-congruence Proofs and congruent triangles.
Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.
13 Similar triangles Similar triangles
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.
14 Similar triangles Using similar triangles to calculate lengths
Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles.
15 Overlapping triangles Examples involving overlapping triangles
Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles.
16 Geometry – triangles Triangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
18 Pythagoras Find the hypotenuse
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.
19 Pythagoras Pythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
20 Pythagoras Find the hypotenuse Part 2
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.
21 Pythagoras Calculating a leg of a right-angled triangle
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.
22 Geometry To identify collinear points, coplanar lines and points in 2 and 3 dimensions
Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.
23 Geometry – angles To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra
Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles.
24 Geometry-constructions Angle bisector construction and its properties (Stage 2)
Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge.
25 Geometry-constructions Circumcentre and incentre (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values.
26 Geometry-constructions Orthocentre and centroids (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
28 Geometry-quadrilaterals Using the Properties of a Parallelogram
Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.
29 Geometry-quadrilaterals Proving a Shape is a Parallelogram
Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.
30 Geometry-quadrilaterals Properties of the Rectangle, Square and Rhombus
Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.
31 Geometry-quadrilaterals Properties of the Trapezium and Kite
Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.
Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties.
33 Geometry-locus Constructions and loci – single condition
Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.
34 Geometry-locus Constructions and loci – multiple conditions
Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.
35 Vectors Vectors
Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram.
36 Vectors 2 vector addition in 2 and 3D (stage 2)
Objective: On completion of the lesson the student will understand and use component forms for vector resolution.
37 Polar coordinates Plotting polar coordinates and converting polar to rectangular
Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system.
38 Polar coordinates Converting rectangular coordinates to polar form
Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates.
39 Polar coordinates Write and graph points in polar form with negative vectors (Stage 2)
Objective: On completion of the lesson the student will be using negative angles and negative vector lengths.
40 Logic Inductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
41 Logic Definition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
42 Logic Indirect proofs
Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved.
43 Logic Mathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
44 Logic Conditional statements (converse, inverse and contrapositive) (Stage 2)
Objective: On completion of the lesson the student will be able to form related conditional statements.
45 Circle Geometry Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs.
Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro
46 Circle Geometry Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord.
Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’
47 Circle Geometry Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal.
Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre.
48 Circle Geometry Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc.
Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.
49 Circle Geometry Theorem – Angles in the same segment of a circle are equal.
Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal.
50 Circle Geometry Theorem – The angle of a semi-circle is a right angle.
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’
51 Circle Geometry Theorem – The opposite angles of a cyclic quadrilateral are supplementary.
Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary.
52 Circle Geometry Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle.
Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite.
53 Circle Geometry Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact.
Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact.
54 Circle Geometry Theorem – Tangents to a circle from an external point are equal.
Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal.
55 Circle Geometry Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
56 Circle Geometry-cyclic quads Theorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic.
Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem.
57 Exam Exam – Year 11 – 13: Planar Geometry
Objective: Exam