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Properties and constructions
Properties and constructions covers geometric notation, angle facts, polygons, loci and formal construction steps, with reasons used to support each conclusion.
25
Objectives
125
Flashcards
125
Questions
90 min
Study time
AQAGCSEMathematicsGeometry and measures
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Syllabus checklist
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25 objective pages available
Geometric terms and notation2 objectives
- [Foundation and Higher] Use conventional geometric terms and notation for points, lines, vertices, edges, planes, angles, polygons and symmetries.
- [Foundation and Higher] Use standard conventions for triangle sides and angles and draw diagrams from written descriptions.
Constructions and loci3 objectives
- [Foundation and Higher] Use standard ruler and compass constructions, including perpendicular bisectors, perpendiculars and angle bisectors.
- [Foundation and Higher] Use constructions to construct figures and solve loci problems.
- [Foundation and Higher] Know that perpendicular distance from a point to a line is the shortest distance to the line.
Angle facts3 objectives
- [Foundation and Higher] Apply angle facts at a point, on a straight line and for vertically opposite angles.
- [Foundation and Higher] Use alternate and corresponding angles on parallel lines.
- [Foundation and Higher] Derive and use angle sums in triangles and polygons and properties of regular polygons.
Quadrilaterals, triangles and polygons1 objectives
- [Foundation and Higher] Derive and apply properties and definitions of special quadrilaterals, triangles and other plane figures using appropriate language.
Triangle congruence1 objectives
- [Foundation and Higher] Use basic triangle congruence criteria: SSS, SAS, ASA and RHS.
Geometric reasoning and proof2 objectives
- [Foundation and Higher] Apply angle facts, congruence, similarity and quadrilateral properties to conjecture and derive results about angles and sides.
- [Foundation and Higher] Use known results including Pythagoras' theorem and isosceles base angles to obtain simple proofs.
Transformations and similarity3 objectives
- [Foundation and Higher] Identify, describe and construct congruent and similar shapes, including on coordinate axes, using rotations, reflections, translations and enlargements.
- [Foundation and Higher] Include fractional scale factors where tier-appropriate.
- [Higher only] Include negative scale factors.
Combined transformations2 objectives
- [Foundation and Higher] Describe changes and invariance from combinations of rotations, reflections and translations.
- [Foundation and Higher] Use column vector notation for translations.
Circle definitions and properties2 objectives
- [Foundation and Higher] Identify and apply circle definitions and properties including centre, radius, chord, diameter and circumference.
- [Foundation and Higher] Include tangent, arc, sector and segment where tier-appropriate.
Circle theorems2 objectives
- [Higher only] Apply and prove standard circle theorems concerning angles, radii, tangents and chords.
- [Higher only] Use circle theorems to prove related geometric results.
Coordinate geometry1 objectives
- [Foundation and Higher] Solve geometrical problems on coordinate axes.
Properties of three-dimensional shapes1 objectives
- [Foundation and Higher] Identify properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres.
Plans and elevations2 objectives
- [Foundation and Higher] Interpret plans and elevations of three-dimensional shapes.
- [Foundation and Higher] Construct plans and elevations of three-dimensional shapes where tier-appropriate.
Key terms
linestandardconstructionshortest distanceanglequadrilateralcongruencePythagorascongruentfoundationhighercolumn vector
Exam tips
- Geometric terms and notation exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Use conventional geometric terms and notation for points, lines, vertices, edges, planes, angles, polygons and symmetries..
- Geometric terms and notation exam tip 1: Write the method before the answer so the examiner can follow each step. Apply this to [Foundation and Higher] Use standard conventions for triangle sides and angles and draw diagrams from written descriptions..
Common mistakes
- Geometric terms and notation common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Geometric terms and notation.
- Geometric terms and notation common mistake 1: Show the method first, then give the final answer in the required form. Apply this directly to Geometric terms and notation.
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