Geometric reasoning

Objective. Write short logical arguments using established angle facts.

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Learn: the key idea

Geometric reasoning builds a short logical argument by chaining together established angle facts, such as angles on a straight line, angles in a triangle, or parallel line rules, each justified by name. Every step must state the fact used, not just the resulting number, so the argument can be followed and checked. To show angle x equals 50° when it's vertically opposite a 50° angle, write 'x = 50° (vertically opposite angles are equal)'. Always give a reason for every step, never just a calculation.

Worked example

In a triangle, two angles are 55° and 65°. Use geometric reasoning to find the third angle, giving a reason.

1 $Recall that angles in a triangle sum to 180°$
2 $Add the known angles: 55 + 65 = 120$
3 $Subtract from 180°: 180 - 120 = 60$
4 $The third angle is 60° (angles in a triangle sum to 180°)$

Answer: 60°

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Common mistake. Pupils often state only the numerical answer without naming the angle fact used, losing marks for an unexplained jump such as writing 'x = 130°' with no reasoning given. Always name the specific angle rule, such as 'angles on a straight line sum to 180°', alongside each step.

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