Content:
MA4-GEO-C-01
Classify triangles according to their side and angle properties
- Label triangles using appropriate text and symbols
- Classify and describe types of triangles based on their properties, including acute-angled, right-angled, obtuse-angled, equilateral, isosceles and scalene triangles
Classify quadrilaterals and describe their properties
- Identify quadrilaterals using naming conventions
- Distinguish between convex and non-convex quadrilaterals
- Verify and describe the properties of the special quadrilaterals which include parallelograms, rectangles, rhombuses, squares, trapeziums and kites
- Identify and label the properties of the special quadrilaterals using appropriate conventions
- Classify quadrilaterals based on their properties
- Justify why some quadrilaterals may be classified as more than one type of quadrilateral
Apply the properties of triangles and quadrilaterals
- Prove that the interior angle sum of a triangle is 180° with or without digital tools
- Prove that any exterior angle of a triangle equals the sum of the 2 interior opposite angles
- Apply the angle sum of a triangle to prove that the angle sum of a quadrilateral is 360°
- Apply the properties of triangles and quadrilaterals to determine unknown sides and angles to solve problems, giving reasons
MA5-GEO-C-01
Identify and describe the properties of similar figures
- Describe similar figures as having the same shape but not necessarily the same size
- Verify and explain that in similar polygons, the corresponding angles are equal and the corresponding side lengths are in the same proportion
- Name the vertices in matching order when using the similar symbol \( (\sim) \) in a similarity statement
- Match the corresponding sides and angles of similar polygons
Solve problems using ratio and scale factors in similar figures
- Apply an appropriate scale to enlarge or reduce a diagram
- Determine the scale factor for pairs of similar polygons and circles
- Apply knowledge of scale factor to find unknown sides in similar polygons
- Solve problems involving unknown lengths and scale factors of similar figures and related practical problems
- Solve problems involving scale drawings, with or without digital tools
MA5-GEO-P-01
Identify and explain congruence
- Identify figures as congruent figures if translations, reflections and rotations can move one figure exactly on top of another
- Match the sides and angles of 2 congruent polygons
- Indicate 2 polygons are congruent using the symbol \( (\equiv) \) and name the vertices in matching order
- Determine that having equal radii is the condition for 2 circles to be congruent
Develop and use the conditions for congruent triangles
- Establish the 4 congruence tests for triangles (SSS, SAS, AAS and RHS)
- Use the congruence tests to identify a pair of congruent triangles from a selection of 2 or more triangles
Develop and apply the minimum conditions for triangles to be similar
- Examine the minimum conditions needed and establish the 4 tests for 2 triangles to be similar
- Apply the minimum conditions needed and determine whether 2 triangles are similar using an appropriate test
Establish and apply properties of similar shapes and solids
- Establish for 2 similar figures with similarity ratio \( a:b \) that their areas are in the ratio \( a^2:b^2 \) and their volumes are in the ratio \( a^3:b^3 \)
- Solve problems involving areas and volumes of similar shapes and solids
Apply logical reasoning to numerical problems involving plane shapes
- Apply geometrical facts, properties and relationships to find the sizes of unknown sides and angles of plane shapes in diagrams, providing appropriate reasons
- Define the exterior angle of a convex polygon
- Establish the sum of the exterior angles of any convex polygon is \( 360^\circ \) and verify this result
- Apply the result for the sum of the interior angles of a triangle to find, by dissection, the sum of the interior angles of a polygon with more than 3 sides
- Apply the results for the interior and exterior angles of polygons to solve problems involving polygons
