- MA5-GEO-P-01 establishes conditions for congruent triangles and similar triangles and solves problems relating to properties of similar figures and plane shapes
📖 Prior Knowledge
| Content | Prior knowledge | Used for |
|---|---|---|
| Ratios and Rates | - problems involving ratios | - properties of similar shapes and solids |
| Right-angled Triangles | - identifying hypotenuse - calculating sides of a right-angled triangle | - congruence and similarity proofs |
| Properties of Geometrical Figures | - angle relationships in triangles and quadrilaterals | - congruence and similarity proofs |
| Area and Surface Area B | - area and surface area of plane shapes | - problems involving surface area of similar solids |
| Properties of Geometrical Figures A | - similarity | - properties of similar shapes and solids |
| Volume B | - volumes of prisms, pyramids, spheres | - problems involving volumes of similar solids |
| Linear Relationships C | - translations, reflections, rotations | - congruence |
Identify and explain congruence.pdf
- 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 (≡) 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.pdf
- 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.pdf
- 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.pdf
- Establish for 2 similar figures with similarity ratio that their areas are in the ratio and their volumes are in the ratio
- Solve problems involving areas and volumes of similar shapes and solids
Apply logical reasoning to numerical problems involving plane shapes.pdf
- 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° 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