LCHL Revision of JC synthetic geometry - Constructions 6,7,10,11,12, Axiom 4, Theorem 2
LCHL Revision of JC synthetic geometry - Theorems 3, *4, 5, *6, 7 & 8
LCHL Revision - Constructions 1, 2, 3 & 4
LCHL Revision: Junior Certificate transformation geometry
LCHL Revision of quadrilaterals, parallelograms, Theorems *9 & 10, Corollary 1and Construction 20
LCHL Revision: More on quadrilaterals
LCHL **Theorem 12 and **Theorem 13
LCHL Introduction to area, Theorem 16, Definition 38, Theorem 17 and Theorem 18
Constructions and how to apply these in real-life situations. Dynamic geometry software. The instruments that are used to perform constructions with precision.
Teachnet Resource
Constructions: Video, Animation, Step-by-step guide & Worksheet
Interactive Files & Worksheets for Geometry & Trigonometry from the Project Maths Website
I should be able to:
At each syllabus level, knowledge of geometrical results from the corresponding syllabus level at Junior Certificate is assumed. Click Here to Revise the Junior Cert Topics.
Foundation Level
– revisit constructions 4,5,10,13 and 15 in real-life contexts
– draw a circle of given radius
– use the instruments: straight edge, compass, ruler, protractor and set square appropriately when drawing geometric diagrams
Ordinary Level
– revisit constructions 1,2,5,6, 8-15 & axioms 1,2,3,4,5, and study the proofs of theorems 1, 2, 3, 4, 5, 6, 9, 10, 13 (statement only), 14, 15; and direct proofs
of corollaries 3, 4. from Junior Cert
– perform constructions 16-21 (see Geometry for Post-primary School Mathematics for Teachers)
– use the following terms related to logic and deductive reasoning: theorem, proof, axiom, corollary, converse, implies
– investigate theorems 7, 8, 11, 12, 13, 16, 17, 18, 20, 21 and corollary 6 (see Geometry for Post-primary School Mathematics for Teachers) and use them to solve problems (No Proofs are examinable)
Higher Level
– revisit constructions 1- 15 & theorems & axioms 1, 2, 3, 4, 5 & the proofs of Theorems 1, 2, 3, 4*, 5, 6*, 9*, 10, 11, 12, 13, 14*, 15, 19*, Corollaries 1, 2, 3, 4, 5, and their converses. Those marked with a * may be asked in examination as from Junior Cert?
– perform construction 16-22 (see Geometry for Post-primary School Mathematics for Teachers)
– use the following terms related to logic and deductive reasoning: is equivalent to, if and only if, proof by contradiction
– prove theorems 11,12,13, concerning ratios (see Geometry for Post-primary School Mathematics for Teachers), which lay the proper foundation for the proof of the theorem of Pythagoras studied at junior cycle
Overview of LCHL Geometry
Proofs of Required Theorems for LCHL
Proofs of Theorems Learned at JCHL that may still be required at LCHL
Khan Academy Lessons & Exercises
Khan Academy proves Pythagoras' Theorem
Junior Cert Theorems View Download
Theorems & Constructions Checklist View
Project Maths Site for Geometry Booklet
LCOL Theorems in your own Words