Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Technical drawing wikipedia , lookup
Multilateration wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
1 WORK PROGRAM MQ 9 NSW 5.1 pathway Chapter 2 Angles and shapes Strand: Space and geometry Substrands and Outcomes: Two-dimensional space SGS3.2a Manipulates, classifies and draws two-dimensional shapes and describes their features Two-dimensional space SGS3.2b Measures, constructs and classifies angles Angles SGS4.2 Identifies and names angles formed by the intersection of straight lines, including those related to transversals on sets of parallel lines, and makes use of the relationships between them Properties of geometrical figures SGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals Section Are you ready? (page 44) GC tips, Investigations, History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles SkillSHEETS, WorkSHEETS, Interactive games, Test yourself, Topic tests (CD–ROM) SkillSHEETS (page 44) 2.1: Classifying angles 2.2: Classifying triangles according to the lengths of their sides 2.3: Naming angles 2.5: Complementary angles 2.6: Supplementary angles 2.13: More angle relations Technology applications (CD–ROM) Learning outcomes SGS3.2a naming isosceles, equilateral and scalene triangles SGS3.2b classifying angles as right, acute, obtuse, reflex, straight or a revolution SGS4.2 naming angles using A and XYZ notation identifying angles of a complete revolution, embedded in a diagram using the words 2 Triangles (page 45) WE 1a-b, 2 Ex 2A Triangles (page 47) SkillSHEET 2.1: Classifying angles (page 48) SkillSHEET 2.2: Classifying triangles according to the lengths of their sides (page 48) Cabri geometry: Classifying triangles (sides) (pages 45, 48) Cabri geometry: Classifying triangles (angles) (pages 46, 48) Mathcad: Classifying triangles (page 48) ‘complementary’ and ‘supplementary’ for angles adding up to 90 and 180 respectively, and the terms ‘complement’ and ‘supplement’ establishing and using the equality of vertically opposite angles SGS4.3 naming triangles (eg ABC) in text SGS4.2 using the common conventions to indicate right angles and equal angles on diagrams SGS4.3 using the common conventions to mark equal intervals on diagrams recognising and classifying types of triangles on the basis of their properties constructing various types of triangles using geometrical instruments, given 3 Angles in a triangle (page 50) WE 3, 4, 5 Ex 2B Angles in a triangle (page 52) Maths Quest challenge: Q1 (page 53) SkillSHEET 2.3: Naming angles (page 52) SkillSHEET 2.4: Angles in a triangle (page 52) Cabri geometry: Angle sum of a triangle (page 52) Mathcad: Angles in a triangle (page 52) Cabri geometry: Angles in right-angled triangles (page 52) Exterior angles of a triangle (page 54) Investigation: Exterior angles of a triangle SkillSHEET 2.5: Complementary angles Cabri geometry: Exterior angles of a triangle different information recognising that a given triangle may belong to more than one class (Reasoning) SGS4.2 labelling and naming angles using A and XYZ notation using dynamic geometry software to investigate angle relationships (Applying strategies, Reasoning) SGS4.3 labelling and naming triangles (eg ABC) in text and on diagrams justifying informally that the interior angle sum of a triangle is 180 applying geometrical facts, properties and relationships to solve numerical problems such as finding unknown angles in diagrams (Applying strategies) SGS4.2 4 WE 6a-b, 7, 8 Ex 2C Exterior angles of a triangle (page 56) Constructing triangles (page 58) WE 9, 10, 11 Ex 2D Constructing triangles (page 60) (page 54) (page 56) SkillSHEET 2.6: Supplementary angles (page 56) (pages 54, 56) Mathcad: Exterior angles of a triangle (page 56) SkillSHEET 2.7: Measuring and drawing lines (page 60) SkillSHEET 2.8: Constructing angles with a protractor (page 60) WorkSHEET 2.1 (page 60) Cabri geometry: Three sides (page 60) Cabri geometry: Two angles and a side (page 60) Cabri geometry: Two sides and an angle labelling the vertex and arms of an angle with capital letters labelling and naming angles using A and XYZ notation using dynamic geometry software to investigate angle relationships (Applying strategies, Reasoning) SGS4.3 justifying informally that any exterior angle equals the sum of the two interior opposite angles applying geometrical facts, properties and relationships to solve numerical problems such as finding unknown angles in diagrams (Applying strategies) SGS4.3 constructing various types of triangles using geometrical instruments, given different information 5 Quadrilaterals (page 61) WE 12a-b Ex 2E Constructing triangles (page 62) Maths Quest challenge: Q1 (page 63) 10 Quick Questions 1 (page 64) between (page 60) Cabri geometry: Squares (page 61) Cabri geometry: Rectangles (page 61) Cabri geometry: Rhombuses (page 61) Cabri geometry: Parallelograms (page 61) Cabri geometry: Trapeziums (page 61) Cabri geometry: Kites (page 61) Cabri geometry: Types of quadrilaterals (page 62) Mathcad: Classifying quadrilaterals (page 62) SGS4.2 using common symbols for ‘is parallel to’ ( ) and ‘is perpendicular to’ ( ) SGS4.3 using the common conventions to mark equal intervals on diagrams constructing various types of quadrilaterals investigating the properties of special quadrilaterals investigating the line symmetries and the order of rotational symmetry of the special quadrilaterals classifying special quadrilaterals on the basis of their properties using dynamic geometry software to investigate the properties of geometrical figures (Applying strategies, Reasoning) 6 Angles in a quadrilateral (page 65) WE 13, 14 Ex 2F Angles in a quadrilateral (page 66) Angles and parallel lines (page 68) WE 15a-b, 16 Ex 2G Angles and parallel lines (page 71) Investigation: Angle relationships with parallel lines (page 69) Maths Quest challenge: Q1-2 (page 73) Investigation: Geometry and the Sydney Harbour Bridge (page 74) SkillSHEET 2.9: Angle sum of a quadrilateral (page 66) Game time 001 (page 67) WorkSHEET 2.2 (page 67) Cabri geometry: Angles in a quadrilateral (page 65) Mathcad: Angles in a quadrilateral (page 66) Cabri geometry: Angle sum of a quadrilateral (page 66) Cabri geometry: Angles in a quadrilateral (page 66) SkillSHEET 2.10: Angles and parallel lines (page 71) Cabri geometry: Corresponding angles (page 68) Cabri geometry: Cointerior angles (page 69) Cabri geometry: Alternate angles (page 69) Cabri geometry: Parallel SGS4.2 using dynamic geometry software to investigate angle relationships (Applying strategies, Reasoning) SGS4.3 distinguishing between convex and nonconvex quadrilaterals establishing that the angle sum of a quadrilateral is 360 investigating the properties of special quadrilaterals applying geometrical facts, properties and relationships to solve numerical problems such as finding unknown angles in diagrams (Applying strategies) SGS4.2 labelling and naming angles using A and XYZ notation identifying and naming a pair of parallel lines and a transversal 7 Code puzzle (page 75) 10 Quick Questions 2 (page 76) lines (pages 69, 71) using common symbols for ‘is parallel to’ ( ) and ‘is perpendicular to’ ( ) using the common conventions to indicate parallel lines on diagrams identifying, naming and measuring the alternate angle pairs, the corresponding angle pairs and the cointerior angle pairs for two lines cut by a transversal recognising the equal and supplementary angles formed when a pair of parallel lines are cut by a transversal using angle properties to identify parallel lines using angle relationships to find unknown angles in diagrams finding the unknown angle in a diagram using angle results, giving reasons 8 Parts of a circle (page 77) WE 17 Ex 2H Parts of a circle (page 79) Angle review (page 80) Ex 2I Angle review (page 80) SkillSHEET 2.11: Using a pair of compasses to draw circles (page 79) SkillSHEET 2.12: Measuring angles with a protractor (page 79) Game time 002 (page 79) Maths Quest challenge: Q1 (page 83) Investigation: SkillSHEET 2.13: More angle relations (page 80) WorkSHEET 2.3 (page 83) (Applying strategies, Reasoning) using dynamic geometry software to investigate angle relationships (Applying strategies, Reasoning) SGS3.2a creating circles by finding points that are equidistant from a fixed point identifying and naming parts of a circle, including the centre, radius, diameter, circumference, sector, semi-circle and quadrant SGS4.2 labelling and naming points, lines and intervals using capital letters SGS4.3 identifying and naming parts of the circle and related lines, including arc, tangent and chord SGS4.2 identifying and naming adjacent angles, 9 Parliamentary question time (page 83) vertically opposite angles, straight angles and angles of complete revolution, embedded in a diagram using the words ‘complementary’ and ‘supplementary’ for angles adding up to 90 and 180 respectively, and the terms ‘complement’ and ‘supplement’ establishing and using the equality of vertically opposite angles identifying, naming and measuring the alternate angle pairs, the corresponding angle pairs and the cointerior angle pairs for two lines cut by a transversal recognising the equal and supplementary angles formed when a pair of parallel lines are cut by a transversal using angle properties to identify parallel 10 lines using angle relationships to find unknown angles in diagrams finding the unknown angle in a diagram using angle results, giving reasons (Applying strategies, Reasoning) SGS4.3 using a parallel line construction, to prove that the interior angle sum of a triangle is 180 proving, using a parallel line construction, that any exterior angle of a triangle is equal to the sum of the two interior opposite angles Summary (page 84) Chapter review (page 86) ‘Test yourself’ multiple choice questions (page 88) Topic tests (2)