Leaving Cert Maths Theorems

Using Geogebra, get access to interactive examples of all Leaving Cert Maths theorems. All links are below to each individual theorem.  Also, find activities at the end.

Source: https://www.projectmaths.ie/for-students/junior-certificate/ 

  • Theorem 7

The angle opposite the greater of two sides is greater than the angle opposite the lesser side.

Conversely, the side opposite the greater of the two angles is greater than the side opposite the lesser angle.


  • Theorem 8

Two sides of a triangle are together greater than the third.


  • Theorem 11 – *** Proofs (HL only) (image below)

To investigate whether, if three parallel lines cut off equal segments on some

transversal line, they cut off equal segments on any other transversal.


Leaving Cert Maths Theorem 11
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  • Theorem 12 – *** Proofs (HL only) (image below)

Let ΔABC be a triangle. If the line t is parallel to BC and cuts [AB] in the ratio m:n,

then it also cuts [AC] in the same ratio.


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  • Theorem 13. *** Proofs (HL only) (image below)

If two triangles are similar, then their sides are proportional, in order.


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  • Theorem 16. For a triangle, base times height does not depend on choice of base.


  • Theorem 17. A Diagonal of a parallelogram bisects the area.


  • Theorem 18. The area of a parallelogram is the base by the height.


  • Theorem 20. Each tangent is perpendicular to the radius that goes to the point of contact.

If P lies on S, and a line l is perpendicular to the radius to P, then l is tangent to S.


  • Theorem 21

(i) The perpendicular from the centre to a chord bisects the chord.

(ii) The perpendicular bisector of a chord passes through the centre.


Here are exercises to practice all of the theorems above and to put them into practice!

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