Reasoning and proof in geometry
Drag an isosceles triangle and see that its base angles always stay equal. Then prove it with reasons, use it in a new proof, and show that another claim is false with a counterexample.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- UK: Year 9
- France: grade 7
- Germany: grade 7
- Iran: grade 9
- Afghanistan: grade 8
- Syria: grade 7
- Palestine: grade 6
- Ukraine: grade 7
- Russia: grade 7
Guide
This studio is for Year 9 (KS3 "use known results to obtain simple proofs").
Measuring a few shapes (inductive reasoning) helps us make a conjecture, but it doesn't prove it: there might be a shape we haven't tried. In deductive reasoning we start from what we are given and reach what we want to prove step by step, with a correct reason for every step. Then the result is true for every shape.
In the proof table every line has a statement and a reason: given, something we constructed (like the midpoint of a side), a common side, a congruence condition, corresponding parts, or a theorem that has already been proved. "It looks equal in the picture" is not a reason, and the thing you are proving can't be its own reason.
To show that a general claim is false, one counterexample is enough.