About this topic
Before you begin
Use angle and symmetry properties, construct triangles and bisectors, and match corresponding parts in congruent or similar figures.
Learning goals
- Classify angles by their size
- Apply the sum of angles around a point
- Deduce all unknown angles at two intersecting lines
- Deduce unknown angles from geometric relationships
- Produce complete parallel-line angle relations and values from numerical or affine-expression givens
- Give the number of lines of symmetry and the order of rotational symmetry of a plane figure
- Classify shapes by their properties
- Connect triangle, rectangle and square facts to deduce angles in a drawn composite figure
- Connect parallelogram and connected shape facts to deduce angles using existing lines
- Connect trapezium and connected shape facts to deduce angles using existing lines
- Construct geometric figures from stated conditions
- Use the equal-distance properties of perpendicular bisectors and angle bisectors
- Reason about congruence, similarity and scale factors
- Find a scale factor and unknown lengths from matched sides of similar triangles
Syllabus statements covered
- Right, acute, obtuse and reflex angles
- Vertically opposite angles, angles on a straight line and angles at a point
- Angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- Properties of triangles, special quadrilaterals
- Properties of perpendicular bisectors of line segments and angle bisectors
- Construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate
- Line and rotational symmetry of plane figures
- Lines of symmetry
- Order of rotational symmetry
- Congruent and similar figures
- Properties of similar triangles and quadrilaterals: ∗ corresponding angles are equal ∗ corresponding sides are proportional
- Right, acute, obtuse and reflex angles
- Vertically opposite angles, angles on a straight line and angles at a point
- Angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- Line and rotational symmetry of plane figures
- Lines of symmetry
- Order of rotational symmetry
- Properties of triangles and special quadrilaterals
- Properties of perpendicular bisectors of line segments and angle bisectors
- Construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractor where appropriate
- Congruent and similar figures
- Properties of similar triangles and quadrilaterals:
- Corresponding angles are equal
- Corresponding sides are proportional
Choose a lesson
Work through them in order.
- Not startedParallel lines and angle reasonsNextName the geometric condition before using an angle equality or sum.
- Not startedAngle relations and equationsNextTrace every angle pair, choose equality or a sum, and check algebraic results against the geometry.
- Not startedLine and rotational symmetryNextTest the whole figure under a reflection or rotation and count matching positions in a full turn.
- Not startedTriangle angle propertiesNextUse the angle sum and equal-side markings to justify unknown triangle angles.
- Not startedParallel quadrilaterals and their anglesNextUse marked parallel sides and named quadrilateral properties to justify unknown angles.
- Not startedTriangle construction from dataNextConstruct a triangle from stated lengths or angles and check that the data determine a possible figure.
- Not startedBisectors and geometric constructionNextUse equal distances to justify compass constructions and check the given dimensions.
- Not startedCongruence and similarityNextMatch corresponding parts before comparing lengths, angles and scale.
- Not startedSimilar triangles and unknown lengthsNextMatch corresponding vertices, find the scale factor and calculate unknown sides in separate, nested and crossed triangles.
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