Points, lines and angles

This lesson comprises three (3) master classes focusing on:

• Points in the Cartesian plane
• Lines in the Cartesian plane
• Transversal and parallel lines
• Measuring and classifying angles
• Circles and elements of

Content:

MA4-LIN-C-01

Plot and identify points on the Cartesian plane

• Plot and label points on the Cartesian plane of given coordinates, including those with coordinates that are not whole numbers
• Identify and record the coordinates of given points on the Cartesian plane, including those with coordinates that are not whole numbers

MA5-LIN-C-01

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane

• Plot and join 2 points to form an interval on the Cartesian plane and use the interval as the hypotenuse of a right-angled triangle
• Apply the relationship gradient \( m=\frac{rise}{run} \)to find the gradient/slope of the interval joining the 2 points
• Distinguish between intervals with positive and negative gradients from a diagram
• Explain why horizontal intervals have a gradient of 0 and vertical intervals have undefined gradients using the gradient relationship
• Determine the midpoint of horizontal and vertical intervals on the Cartesian plane
• Apply the process for calculating the mean to find the midpoint, of the interval joining 2 points on the Cartesian plane
• Use graphing applications to find the midpoint and gradient/slope of an interval

Find the distance between 2 points located on the Cartesian plane

• Use the interval between 2 points as the hypotenuse of a right-angled triangle on the Cartesian plane and apply Pythagoras’ theorem to determine the length of the interval joining the 2 points
• Use graphing applications to find the distance between 2 points on the Cartesian plane

MA4-ANG-C-01

Apply the language, notation and conventions of geometry

• Use appropriate terminology and conventions to define, label and name points, rays, lines and intervals using capital letters
• Identify and label the vertex and arms of an angle with capital letters
• Use appropriate conventions to label and name angles
• Use common conventions to indicate right angles, equal angles and intervals on diagrams

Identify geometrical properties of angles at a point

• Identify right angles, straight angles, angles of complete revolution and vertically opposite angles
• Apply the terms complementary and supplementary to a pair of angles adding to \( 90^{\circ} \) and \( 180^{\circ} \), respectively
• Apply the term adjacent angles to a pair of angles with a common arm and common vertex

Identify and describe corresponding, alternate and co-interior angles when 2 straight lines are crossed by a transversal, including parallel lines

• Identify and describe perpendicular lines using the symbol for is perpendicular to (\(\perp\))
• Apply the common conventions to indicate parallel lines on diagrams
• Identify and describe pairs of parallel lines using the symbol for is parallel to (\(\parallel\))
• Identify and define transversals, including transversals of parallel lines
• Identify, name and measure alternate angle pairs, corresponding angle pairs and co-interior angle pairs for 2 lines cut by a transversal
• Verify and identify corresponding angles and alternate angles as equal, and co-interior angles as supplementary, when a pair of parallel lines is cut by a transversal
• Justify that 2 lines are parallel by using properties of alternate, corresponding or co-interior angles on parallel lines

Solve numerical problems involving angles using reasoning

• Apply the knowledge of angle relationships including angles at a point to find the sizes of unknown angles embedded in diagrams and give reasons
• Apply the knowledge of angles associated with parallel lines to find the sizes of unknown angles embedded in related diagrams and give reasons