About this topic
Before you begin
Prove congruence, similarity, circle, midpoint and tangent–chord relationships, state the conditions each step needs and test claims with counterexamples.
Learning goals
- Construct a geometric argument or proof
- Find a scale factor and unknown lengths from matched sides of similar triangles
- Reason about congruence, similarity and scale factors
Syllabus statements covered
- Properties of parallel lines cut by a transversal, perpendicular and angle bisectors, triangles, special quadrilaterals and circles
- Congruent and similar triangles
- Midpoint theorem
- Tangent-chord theorem (alternate segment theorem) (The first two properties are learnt in G3 Mathematics.)
- Properties of parallel lines cut by a transversal, perpendicular and angle bisectors, triangles, special quadrilaterals and circles
- Congruent and similar triangles
- Midpoint theorem
- Tangent-chord theorem (alternate segment theorem)
Choose a lesson
Work through them in order.
- Not startedCongruence, similarity and circle proofsNextChoose the triangles that contain the target, justify congruence or similarity with exact correspondences and use circle properties only in their stated configurations.
- Not startedMidpoint and tangent–chord proofsNextDerive midpoint relationships, distinguish alternate segments and build a non-circular proof with a missing-condition counterexample.