Geometry: Proofs & Theorems
Geometry proofs build logical reasoning skills used in all of mathematics. Learn the key theorems about angles, triangles, and parallel lines — and practice constructing arguments.
Key Concepts
Two-Column Proofs
A proof has Statements (what we claim is true) and Reasons (the rule that justifies it). Common reasons: Given, Definition, Postulate, Theorem, Algebra Properties.
Parallel Lines & Transversals
When a transversal cuts two parallel lines: alternate interior angles are equal, corresponding angles are equal, co-interior (same-side) angles are supplementary (sum to 180°).
Triangle Theorems
Triangle Angle Sum: angles sum to 180°. Exterior Angle: equals sum of the two non-adjacent interior angles. Pythagorean Theorem: a²+b²=c² for right triangles.
Congruence & Similarity
Congruent triangles have same shape & size (SSS, SAS, ASA, AAS). Similar triangles have same shape, proportional sides (AA, SAS~, SSS~). Scale factor = ratio of corresponding sides.
Live Python Practice
Interactive Lab
Check Your Understanding
When two parallel lines are cut by a transversal, alternate interior angles are:
The exterior angle of a triangle equals:
Two triangles are congruent by SAS if they share: