YEAR 7 MATHS FOCUS
MEASUREMENT AND GEOMETRY
ANGLE RELATIONSHIPS
OUTCOME
A student:
MA418MG:
identifies and uses angle relationships, including those related to transversals on sets of parallel lines
TEACHING POINTS  Students could explore the results relating to angles associated with parallel lines cut by a transversal by starting with corresponding angles and moving one vertex and all four angles to the other vertex by a translation. The other two results then follow, using vertically opposite angles and angles on a straight line. Alternatively, the equality of the alternate angles can be seen by rotation about the midpoint of the transversal. Students should give reasons when finding the sizes of unknown angles. For some students, formal setting out could be introduced. For example, ∠ABQ=70∘ (corresponding angles, AC∥PR). In his calculation of the circumference of the Earth, the Greek mathematician, geographer and astronomer Eratosthenes (c276–c194 BC) used parallel line results. 
LANGUAGE  Students in Stage 4 should write geometrical reasons without the use of abbreviations to assist them in learning new terminology, and in understanding and retaining geometrical concepts, eg ‘When a transversal cuts parallel lines, the cointerior angles formed are supplementary’. Some students may find the use of the terms ‘complementary’ and ‘supplementary’ (adjectives) and ‘complement’ and ‘supplement’ (nouns) difficult. Teachers should model the use of these terms in sentences, both verbally and in written form, eg, ’50° and 40° are complementary angles’, ‘The complement of 50° is 40°’. Students should be aware that complementary and supplementary angles may or may not be adjacent. 
PURPOSE RELEVANCE OF SUBSTRAND  The development of knowledge and understanding of angle relationships, including the associated terminology, notation and conventions, is of fundamental importance in developing an appropriate level of knowledge, skills and understanding in geometry. Angle relationships and their application play an integral role in students learning to analyse geometry problems and developing geometric and deductive reasoning skills, as well as problemsolving skills. Angle relationships are key to the geometry that is important in the work of architects, engineers, designers, builders, physicists, land surveyors, etc, as well as the geometry that is common and important in everyday situations, such as in nature, sports, buildings, astronomy, art, etc. 
Expectations of Attainment
Use the language, notation and conventions of geometry  define, label and name points, lines and intervals using capital letters 
label the vertex and arms of an angle with capital letters  
label and name angles using ∠P or ∠QPR notation  
use the common conventions to indicate right angles and equal angles on diagrams 
Recognise the geometrical properties of angles at a point  use the terms ‘complementary’ and ‘supplementary’ for angles adding to 90° and 180°, respectively, and the associated terms ‘complement’ and ‘supplement’ 
use the term ‘adjacent angles’ to describe a pair of angles with a common arm and a common vertex, and lie on opposite sides of the common arm  
identify and name right angles, straight angles, angles of complete revolution and vertically opposite angles embedded in diagramsLiteracy Critical and creative thinking

Identify corresponding, alternate and cointerior angles when two straight lines are crossed by a transversal (ACMMG163)  identify and name perpendicular lines using the symbol for ‘is perpendicular to’ (⊥), eg AB⊥CD 
use the common conventions to indicate parallel lines on diagrams  
identify and name pairs of parallel lines using the symbol for ‘is parallel to’ (∥), eg PQ∥RS  
define and identify ‘transversals’, including transversals of parallel lines  
identify, name and measure alternate angle pairs, corresponding angle pairs and cointerior angle pairs for two lines cut by a transversalCritical and creative thinking
 
recognise the equal and supplementary angles formed when a pair of parallel lines is cut by a transversal 
Investigate conditions for two lines to be parallel (ACMMG164)  use angle properties to identify parallel lines Critical and creative thinking

Solve simple numerical problems using reasoning (ACMMG164)  find the sizes of unknown angles embedded in diagrams using angle relationships, including angles at a point and angles associated with parallel lines, giving reasons

Construction of a shape using triangles – start with small tooth picks and small rubber bands, then use bamboo crafted into lengths in the ratio 3, 4, 5
Using Pythagoras theorem to advance the understanding of right angles.
Understanding a line is half a circle – so is 360 / 2 = 180
Angles occur where two intervals intersect – and will have angles formed as a result.