LCOL Geometry
Your progress through this topic0 of 16 lessons
Lessons in this topic
All 16 lessons.
1Theorems, Axioms and Corollaries2Constructions3Constructing the circumcircle4Constructing the incircle5Constructing the Centroid6Angles7Circle Questions8Congruent Triangles9Similar Triangles10Transformations 111Transformations 2 Enlargements12Proof of Theorem 4 (Practise)13Proof of Theorem 6 (Practise)14Proof of Theorem 9 (Practise)15Proof of Theorem 14 (Practise)16Proof of Theorem 19 (Practise)
Key ideas in this topic
★ Must learn
There are 21 theorems on the Leaving Cert Ordinary Level course. At OL you recognise and apply them — you are not asked to prove the hard ones.
LCOL Geometry 1
★ Must learn
An axiom is a statement accepted as true without proof. There are 5 axioms; the one to learn is that a straight angle is 180°.
LCOL Geometry 1
★ Must learn
A corollary is a small result that follows directly from a theorem. There are 6 corollaries (e.g. an angle in a semicircle is 90°).
LCOL Geometry 1
★ Must learn
A slide — every point moves the same distance in the same direction.
LCOL Geometry 11
★ Must learn
A flip in a line — the image is the mirror image in the axis.
LCOL Geometry 11
★ Must learn
A flip through a point — every point passes through the centre to the far side.
LCOL Geometry 11
★ Must learn
A turn about a point through an angle.
LCOL Geometry 11
★ Must learn
A scaling by a factor from a centre — every length is multiplied by the scale factor.
LCOL Geometry 11
★ Must learn
There are 21 constructions on the Ordinary Level course, done with compass and straight edge only — measuring the answer with a protractor earns no marks; the arcs are the marks.
LCOL Geometry 2
★ Must learn
Two angles standing on the same arc (subtended by the same chord) are equal.
LCOL Geometry 7
★ Must learn
Two triangles are congruent (identical) if they match on SSS, SAS, ASA or RHS. Set the proof out in two columns, one triangle each.
LCOL Geometry 8
★ Must learn
Two triangles are similar if their angles are equal and their sides are in proportion. Set up matching ratios to find a missing length.
LCOL Geometry 9