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LC Mathematics
LC Mathematics
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LC Mathematics

Theorems to Learn for Leaving Cert. HL

Theorem: A general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.

1. Vertically opposite angles are equal in measure.

2. In an isosceles triangle the angles opposite the equal sides are equal. Conversely, if two angles are equal, then the triangle is isosceles.

3. If a transversal makes equal alternate angles on two lines then the lines are parallel. Conversely, if two lines are parallel, then any transversal will make equal alternate angles with them.

4.* The angles in any triangle add to 180.

5. Two lines are parallel if,... (More)

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LC Mathematics

Complex numbers: Roots of a cubic equation

A cubic equation can have 3 real roots or 1 real root and a complex conjugate pair. In this video I show you how through the graphs of cubic equations. I then show you how to solve cubic equations that have complex roots by looking at this example:

  • Find all the roots of the equation 

You are then given this question to try.

  • Find all the roots of the equation 


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LC Mathematics

Leaving Cert. Maths Construction Video Tutorials

Angle Bisector

Perpendicular Bisector of Line Segment

Perpendicular through point not on line

Perpendicular through point on line

Line parallel to given line through a point

Division of segment into 2 or 3 equal parts

Division into any number of parts

Segment of given length, on given ray


Triangle SSS

Triangle SAS

Triangle ASA

Triangle RHS

List of constructions to know

  • Bisector of an angle, using only compass and straight edge.
  • Perpendicular bisector of a segment, using only compass and straight edge.
  • Line perpendicular to a given line l, passing through a given point not on l.
  • Line perpendicular... (More)
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LC Mathematics

Axioms, Corollaries & Theorems - Part 1


Axiom: A statement or proposition that is regarded as being established, accepted, or self-evidently true.

  1. Axiom 1: There is exactly one line through any two given points
  2. Axiom 2: [Ruler Axiom]: The properties of the distance between points.
  3. Axiom 3: Protractor Axiom (The properties of the degree measure of an angle).
  4. Axiom 4: Congruent triangles conditions (SSS, SAS, ASA)
  5. Axiom 5: Given any line l and a point P, there is exactly one line through P that is parallel to l.


Corollary: A proposition that follows from (and is often appended... (More)