LCHL Maths – Geometry

Leaving Cert Higher Level Maths LCHL Maths – Geometry

LCHL Geometry

Your progress through this topic0 of 19 lessons

Lessons in this topic

All 19 lessons, in order — each one ticks off as you open it.

1Axioms, Theorems, Corollaries★ Learn off2Construction 1 – 15 , 18, 19, 20★ Learn off3Construction 16 – Circumcircle★ Learn off4Construction 17 – Incircle★ Learn off5Construction 21 – Centroid★ Learn off6Construction 22 – Orthocentre★ Learn off7Proof of Theorem 4★ Learn off8Proof of theorem 6★ Learn off9Proof of Theorem 9★ Learn off10Proof of Theorem 14★ Learn off11Proof of theorem 19★ Learn off12Proof of theorem 11★ Learn off13Proof of theorem 12★ Learn off14Proof of theorem 13★ Learn off15Questions on theorem 19 (circle questions)★ Learn off16Similar Triangles★ Learn off17Congruent Triangles★ Learn off18Rotations, Translations, Central symmetry, Axial symmetry★ Learn off19Enlargements★ Learn off

Key topics to learn off

There’s a lot here — learn the axioms, the theorem proofs, the constructions and the transformations.

5 axioms21 theorems6 corollaries22 constructions3 examinable proofs (Theorems 11, 12, 13)Centroid, circumcentre, orthocentreCongruent & similar trianglesTransformations & enlargements

Key ideas in this topic

★ Must learn
The 21 theorems
The 21 theoremsprove Theorems 11, 12 and 13
★ Must learn
The 6 corollaries
The 6 corollariesCorollary 6 is new at LCHL
★ Must learn
The 5 axioms
The 5 axiomsaccepted without proof
★ Must learn
The 22 constructions
The 22 constructionsGeometry 2
★ Must learn
Circumcentre
CircumcentreGeometry 3 — construction 16
★ Must learn
Orthocentre
OrthocentreGeometry 6 — construction 22
★ Must learn
Centroid
CentroidGeometry 5 — construction 21
★ Must learn
Incircle
IncircleGeometry 4 — construction 17
★ Must learn
Congruent triangles
Congruent trianglesGeometry 17
★ Must learn
Similar triangles
Similar trianglessides proportional in order (Theorem 13)
📖 In the log tables
Pythagoras (Theorem 14)
Pythagoras (Theorem 14)page 16 of the log tables
★ Must learn
The circle theorem
The circle theoremTheorem 19 + Corollaries 2–5

The five transformations

★ Must learn
Translation
Translationevery point moves by the same vector
★ Must learn
Central symmetry
Central symmetryreflection through a point
★ Must learn
Axial symmetry
Axial symmetryreflection in a line
★ Must learn
Rotation
Rotation90° rules about the origin
★ Must learn
Enlargement
Enlargementk, k², k³ — new at LCHL

Check it against the exam

Jump straight to the fully worked solution for that paper.

2023 Paper 1 Q8 →2023 Paper 2 Q6 →2023 Paper 2 Q7 →2022 Paper 2 Q10 →2022 Paper 2 Q6 →

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