Proof Lab
Test statements, find counterexamples and build short proofs.
Proof Lab teaches the logic behind geometry before and during a first proof unit. It begins with if-then statements about numbers, asking students to find the hypothesis and conclusion and to hunt for a counterexample using number tiles. Then it adds the converse, inverse and contrapositive, and which of them always match the original.
From there the game moves into figures. Students name angle pairs made by a transversal, decide whether lines are parallel, and use SSS, SAS, ASA, AAS and HL to judge whether triangles are congruent, including when the marks are not enough. Similar triangles, scale factors and shadow problems follow, and the final level asks students to put the steps of a short proof in order with the right reasons.
What children practice
- Pick out the hypothesis and conclusion of an if-then statement
- Write a converse, inverse and contrapositive and tell which are true
- Find a counterexample with numbers or with a shape
- Name angle pairs and find missing angles when lines are parallel
- Decide whether triangles are congruent by SSS, SAS, ASA, AAS or HL
- Use similar triangles to find a scale factor, a missing side or an area ratio
Levels
- Level 1: If-then statements
- Level 2: Converse and contrapositive
- Level 3: Counterexamples
- Level 4: Angle pairs
- Level 5: Parallel lines
- Level 6: Congruent triangles
- Level 7: Similar triangles
- Level 8: Course mix
How it works
- Eight levels go from if-then statements to similar triangles, and the last level is a proof workshop plus a course mix.
- Figures are drawn from real measurements, so lines that look parallel only look that way when they truly are.
- Getting five questions right and finishing the practice timer moves your child up to the next level.
- Questions use choices, a keypad, tapping parts of a figure, sorting and ordering the steps of a proof.
Best for: A good fit for grades 9 to 10 in a geometry course, especially when a student finds the move from calculating to explaining hard.
Tip for parents: Pick an everyday rule, such as if it rains then the ground is wet, and ask your child to state its converse. Talking through whether the converse is also true is the heart of this game.
Questions parents ask
Does the game teach two-column proofs?
It teaches the pieces of one. Early rounds build the logic of statements and reasons, and the later levels have students put the statements of a short proof in order and match each with its reason.
How does it check a proof when two steps can go in either order?
When two steps do not depend on each other, either order is accepted. Any order that puts every step after the steps it relies on counts as right.
What if a student has not learned triangle congruence yet?
The levels unlock in order, so Levels 1 through 5 can be played first. Congruence arrives at Level 6 and similarity at Level 7, after angle pairs and parallel lines.
Ready to try it?
Proof Lab is free with a parent account. A parent adds a child profile, and the child's progress is saved.