The side-splitting theorem

• Resources Structure
• Key Stage 4
• Mathematics
• II. Geometry and transformations
• 23. Similarity – solving problems
• 21. Similarity – solving problems

• Exam Specifications
• Key Stage 4
• AQA GCSE Mathematics A (4301)
• II. Shape, space and measures
• Geometrical reasoning
• Properties of triangles and other rectilinear shapes
• distinguish between lines and line segments; use parallel lines, alternate angles and corresponding angles; understand properties of parallelograms
• use angle properties of equilateral, isosceles and right-angled triangles; understand congruence; explain why the angle sum of a quadrilateral is 360 degrees
• use their knowledge of rectangles, parallelograms and triangles to deduce formulae for the area of a parallelogram, and a triangle, from the formula for the area of a rectangle
• recall the essential properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric properties
• distinguish between lines and line segments; understand a proof that the angle sum of a triangle is 180 degrees; understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices
• use angle properties of equilateral, isosceles and right-angled triangles; explain why the angle sum of a quadrilateral is 360 degrees
• recall the definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric properties
• calculate and use the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons.
• understand, recall and use Pythagoras' theorem
• understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and to verify standard ruler and compass constructions
• understand, recall and use Pythagoras' theorem in 2-D, then 3-D problems; investigate the geometry of cuboids including cubes, and shapes made from cuboids, including the use of Pythagoras' theorem to calculate lengths in three dimensions
• understand similarity of triangles and of other plane figures; understand, recall and use trigonometrical relationships in right-angled triangles; calculate the area of a triangle; draw, sketch and describe the graphs of trigonometric functions

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