This worksheet formalises geometric reasoning, teaching students to apply established angle and triangle theorems as the justified steps of a deductive proof. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A deductive proof reaches a conclusion by chaining together already-established facts (theorems, definitions, given information) — each step must be justified by a named reason, not just asserted.
- Angle sum of a triangle = 180°. Angle sum of a quadrilateral = 360°. Angle sum of a polygon with n sides = (n−2)×180°.
- Parallel lines cut by a transversal: alternate angles are equal, co-interior angles sum to 180°, and corresponding angles are equal.
- The Exterior Angle Theorem: an exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles.
- Congruence tests (sss, sas, aas, rhs) let you prove two triangles are identical in shape and size — this is often the key step used to prove a broader geometric fact (e.g. isosceles triangle base angles are equal).
What your child will practise:
- Applying the angle sum of a triangle or polygon to find a missing angle.
- Applying parallel-line angle relationships (alternate, co-interior, corresponding, vertically opposite) to find missing angles.
- Applying the Exterior Angle Theorem, and verify it independently against the triangle angle sum.
- Using a congruence test as a justified step within a deductive proof.
- Writing a short chain of justified deductive steps to reach and explain a geometric conclusion.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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