#MeasurementAndSpace #Path #Ext >[!info]- [Properties of geometrical figures B (Path) | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa222c8206) >- 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 | | ---------------------------------------------- | -------------------------------------------------------------------------- | --------------------------------------------------- | | [[Stage 4/Ratios and Rates\|Ratios and Rates]] | - problems involving ratios | - properties of similar shapes and solids | | [[Right-angled Triangles]] | - identifying hypotenuse<br>- 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 $a:b$ 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.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