| # | TOPIC | TITLE | +/- | |
|---|---|---|---|---|
| 1 | Self Assessment | Self Assessment - Grade 8-12 Geometry | Info | Go |
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Objective: Assessment |
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| 2 | Logic | Inductive and Deductive Reasoning | Info | Go |
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Objective: To identify and use inductive and deductive reasoning |
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| 3 | Logic | Mathematical induction | Info | Go |
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Objective: To use proof by mathematical induction |
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| 4 | Logic | Proof by Disproof of a Contradictory Statement | Info | Go |
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Objective: To prove that a statement is true by proving that the contradictory statement is false |
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| 5 | Logic | Disproof of Counter Example | Info | Go |
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Objective: To identify a statement as a counter example to disprove a statement |
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| 6 | Geometry-congruence | Congruent triangles, Test 1 and 2 | Info | Go |
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Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. |
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| 7 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | Info | Go |
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Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS |
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| 8 | Geometry part 2 | Proofs and Congruent Triangles | Info | Go |
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Objective: To use congruency in formal proofs in order to determine unknown angles and sides |
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| 9 | Geometry part 2 | Similar Triangles | Info | Go |
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Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles |
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| 10 | Similar triangles | Using similar triangles to calculate lengths | Info | Go |
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Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. |
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| 11 | Geometry part 2 | Examples involving overlapping triangles | Info | Go |
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Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles |
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| 12 | Geometry part 3 | The Triangle Inequality Theorem | Info | Go |
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Objective: To use the triangle inequality theorem to determine constructability of triangles |
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| 13 | Geometry-angles | Parallel Lines. | Info | Go |
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Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. |
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| 14 | Geometry part 1 | Additional questions involving parallel lines | Info | Go |
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Objective: To determine angle magnitude for angles formed by parallel lines and transversals |
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| 15 | Geometry part 2 | More difficult exercises involving parallel lines | Info | Go |
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Objective: To determine the angles of geometric figures using known properties and theorems |
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| 16 | Geometry part 2 | Further difficult exercises involving formal reasoning | Info | Go |
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Objective: To determine formally angles of geometric figures using known properties and theorems |
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| 17 | Circle geometry part 1 | Theorem - Equal arcs subtend equal angles at the centre | Info | Go |
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Objective: To know that equal arcs on circles of equal radii subtend equal angles at the centre |
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| 18 | Circle geometry part 1 | Theorem - The perpendicular from the centre to a chord bisects the chord | Info | Go |
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Objective: To know that the perpendicular from the centre of a circle to a chord bisects the chord and to know that the line from the centre of a circle to the mid-point of a chord is perpendicular to the chord |
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| 19 | Circle geometry part 1 | Theorem - Equal chords in a circle are equidistant from the centre | Info | Go |
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Objective: To know that equal chords in equal circles are equidistant from the centres |
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| 20 | Circle geometry part 1 | Theorem - The angle at the centre is double the angle at the circumference | Info | Go |
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Objective: To know that the angle at the centre of a circle is double the angle at the circumference standing on the same arc |
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| 21 | Circle geometry part 1 | Theorem: Angles in the same segment of a circle are equal | Info | Go |
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Objective: To know that angles in the same segment of a circle are equal |
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| 22 | Circle Geometry | Theorem - The angle of a semi-circle is a right angle. | Info | Go |
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Objective: On completion of the lesson the student will be able to prove that 'The angle of a semi-circle is a right-angle.' |
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| 23 | Circle geometry part 1 | Theorem: The opposite angles of a cyclic quadrilateral are supplementary | Info | Go |
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Objective: To know that the opposite angles of a cyclic quadrilateral are supplementary |
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| 24 | Circle geometry part 1 | Theorem - Exterior angle of cyclic quadrilateral equals interior opposite angles | Info | Go |
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Objective: To know that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle |
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| 25 | Circle geometry part 1 | Theorem - At the point of contact a tangent is perpendicular to the radius | Info | Go |
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Objective: To know that the tangent to a circle is perpendicular to the radius drawn to it |
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| 26 | Circle geometry part 1 | Theorem: Tangents to a circle from an external point are equal | Info | Go |
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Objective: To know that the tangents to a circle from an external point are equal |
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| 27 | Measurement - Advanced area | Area of a Trapezium | Info | Go |
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Objective: To calculate the area of trapezia using A=(h/2)(a+b) |
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| 28 | Measurement - Advanced area | Area of a Rhombus | Info | Go |
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Objective: To calculate the area of a rhombus using diagonal products |
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| 29 | Measurement - Advanced area | Area of a Circle | Info | Go |
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Objective: To calculate the area of circles and sectors and to solve circle problems |
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| 30 | Measurement - Advanced area | Area of Regular Polygons and Composite Figures | Info | Go |
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Objective: To calculate area of composite figures and solve problems using correct formulae |
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| 31 | Measurement - Advanced volume | Finding the volume of prisms | Info | Go |
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Objective: To calculate the volume of prisms using V=Ah and solve volume problems |
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| 32 | Measurement - Advanced volume | Volume of a Cylinder and Sphere | Info | Go |
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Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each |
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| 33 | Measurement - Advanced volume | Volume of Pyramids and Cones | Info | Go |
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Objective: To calculate the volumes of pyramids and cones |
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| 34 | Surface area | Surface Area of a Cube/Rectangular Prism | Info | Go |
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Objective: To calculate the surface area of cubes and rectangular prisms |
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| 35 | Surface area | Surface area of a triangular/trapezoidal prism. | Info | Go |
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Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. |
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| 36 | Surface area | Surface Area of a Cylinder and Sphere | Info | Go |
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Objective: To calculate the surface area of cylinders and spheres |
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| 37 | Surface area | Surface Area of Pyramids | Info | Go |
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Objective: To calculate the surface area of pyramids |
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| 38 | Surface area | Surface Area of Composite Solids | Info | Go |
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Objective: To calculate the surface area of composite solids |
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| 39 | Surface area | Surface area of composite solids | Info | Go |
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Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. |
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| 40 | Measurement - Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | Info | Go |
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Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height |
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| 41 | Measurement - Area | Finding the Area of a Triangle and Other Composite Shapes | Info | Go |
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Objective: To calculate the area of triangles and measure and calculate composite shape area |
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| 42 | Geometry part 1 | Angle Sum of a Triangle | Info | Go |
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Objective: To use the angle sum for a triangle to calculate unknown angles |
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| 43 | Geometry part 1 | Exterior angle theorem | Info | Go |
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Objective: To use the external angle of a triangle theorem to calculate unknown angles |
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| 44 | Geometry part 1 | Special triangles | Info | Go |
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Objective: To use the properties of equilateral and isosceles triangles to calculate angle size |
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| 45 | Geometry part 1 | Quadrilaterals | Info | Go |
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Objective: To use the angle sum of a quadrilateral to calculate unknown angles |
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| 46 | Quadrilaterals | Quadrilaterals 1 | Info | Go |
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Objective: To recognise, name and describe the properties of quadrilaterals |
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| 47 | Quadrilaterals | Properties of Parallelograms - Opposite Angles Equal | Info | Go |
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Objective: To prove and use 'Opposite angles of a parallelogram are congruent' |
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| 48 | Quadrilaterals | Properties of Parallelograms - Diagonals, Sides and Angles | Info | Go |
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Objective: To prove parallelogram properties and calculate unknown angles and lengths |
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| 49 | Quadrilaterals | The Parallelogram Umbrella | Info | Go |
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Objective: To prove properties of specific parallelograms and find angles and lengths |
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| 50 | Quadrilaterals | Properties of Trapezoids | Info | Go |
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Objective: To prove properties of trapezoids and find unknown lengths and angles |
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| 51 | Geometry-quadrilaterals | The quadrilateral family and coordinate methods in geometry | Info | Go |
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Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. |
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| 52 | Pythagoras | Proofs of Pythagoras' Theorem | Info | Go |
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Objective: To examine and complete proofs of Pythagoras' Theorem |
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| 53 | Pythagoras | Pythagoras' Theorem: Finding the Hypotenuse | Info | Go |
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Objective: To calculate the length of a hypotenuse using Pythagoras' Theorem |
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| 54 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | Info | Go |
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Objective: To identify right triangles by using Pythagorean Triples or Pythagoras' Theorem |
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| 55 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | Info | Go |
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Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals |
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| 56 | Pythagoras | Calculating a Leg of a right-angled Triangle | Info | Go |
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Objective: To calculate the length of sides other than the hypotenuse using Pythagoras' Theorem |
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| 57 | Geometry-constructions | Geometric constructions | Info | Go |
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Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
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| 58 | Geometry part 3 | Points, Lines and Planes | Info | Go |
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Objective: To identify collinear points and coplanar lines and points in 2 and 3 dimensions |
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| 59 | Geometry - angles | To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra | Info | Go |
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Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. |
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| 60 | Geometry part 3 | Angle Bisector Construction and its Properties | Info | Go |
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Objective: To geometrically bisect angles and calculate angle size given bisection |
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| 61 | Geometry part 3 | Circumcenter and Incenter | Info | Go |
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Objective: To use properties of triangles, circles, circumcentres and incentres |
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| 62 | Geometry part 3 | Orthocentre and Centroids | Info | Go |
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Objective: To use properties of triangles, circles orthocentres and centroids |
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| 63 | Trigonometry part 1 | Trigonometric Ratios | Info | Go |
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Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle |
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| 64 | Trigonometry part 2 | Trigonometric Identities | Info | Go |
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Objective: To simplify expressions using trigonometric equalities |
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| 65 | Trigonometry part 1 | Using the Calculator | Info | Go |
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Objective: To determine trigonometric ratios using a calculator |
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| 66 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | Info | Go |
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Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. |
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| 67 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | Info | Go |
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Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle |
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| 68 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | Info | Go |
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Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle |
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| 69 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | Info | Go |
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Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator |
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| 70 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | Info | Go |
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Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees |
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| 71 | Circle geometry part 1 | Theorem - Angle between a tangent and chord equals angle in alternate segment | Info | Go |
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Objective: To know that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment |
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| 72 | Geometry transformations | Geometry Transformations without Matrices: Translation | Info | Go |
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Objective: To find the image of a point or object after a translation |
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| 73 | Geometry transformations | Geometry Transformations without Matrices: Rotation | Info | Go |
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Objective: To determine rotation angle and to perform prescribed rotations |
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| 74 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | Info | Go |
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Objective: To describe dilations and to calculate lengths and scale factors of dilated figures |
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| 75 | Exam | Exam - Grade 8-12 Geometry | Info | Go |
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Objective: Exam |
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