Using GeoGebra, get access to interactive examples of Junior Cert Maths Theorems. All links are below to each individual theorem. Also, find activities at the end.
Geometry and trigonometry ->
- Theorem 1 – Vertically opposite angles are equal in measure.
- Theorem 2 – In an isosceles triangle the angles opposite the equal sides are equal. https://www.projectmaths.ie/geogebra/theorem-2/
- Theorem 3 – If a transversal makes equal alternate angles on two lines then the lines are parallel.
- Theorem 4 – JC HL The angles in any triangle add to 180° (Angle ABC + Angle BCA + Angle CAB = 180°)
- Theorem 5. Two lines are parallel if and only if, for any transversal, the corresponding angles are equal.
- Theorem 6. Each exterior angle of a triangle equals the sum of the interior opposite angles.
- Theorem 9. In a parallelogram, opposite sides are equal and opposite angles are equal.
- Theorem 10. The diagonals of a parallelogram bisect each other.
- Theorem 13. If two triangles are similar then their sides are proportional, in order
- Theorem 14. Theorem of Pythagoras.
In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides.
- Theorem 15. If the square of one side of a triangle is the sum of the squares of the other two, then the angle opposite the first side is a right angle.
- Theorem 11
- Theorem 12. Let ABC be a triangle. If a line l is parallel to BC and cuts [AB] in a ratio m:n,
then it also cuts [AC] in the same ratio.
- Theorem 19. The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.
Here are exercises to practice all of the theorems above and to put them into practice!