We enter the world of geometry. Unlike algebra, here we do not calculate: we prove. The chapter starts from the logical structure of a theorem — hypothesis, thesis, postulates, syllogism — and from a practical method for constructing a proof. From there the whole scaffolding of the two-year Euclidean geometry course develops: the three congruence criteria for triangles, which are the fundamental building block, and then their classic applications (vertically opposite angles, the isosceles triangle, the exterior angle theorem, the sum of the interior angles). We arrive at loci (the perpendicular bisector and the angle bisector), at parallelism with alternate interior angles, at quadrilaterals (trapezium, parallelogram, rhombus, rectangle) and finally at two powerful results: the hinge theorem and the intercept theorem.
Sections
- What is a theorem?
- How to prove a geometry theorem
- Congruence criteria for triangles
- Vertically opposite angles
- The isosceles triangle
- The exterior angle theorem
- The sum of the interior angles of a polygon
- Congruence criteria for right triangles
- Locus
- Parallel lines and angles
- Proofs using parallelism
- The perpendicular bisector of a segment
- Quadrilaterals
- The hinge theorem
- The intercept theorem