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.

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

**Geometry and trigonometry -> **

- Theorem 1 – Vertically opposite angles are equal in measure.

https://www.projectmaths.ie/geogebra/theorem-1/

- 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.

https://www.projectmaths.ie/geogebra/theorem-3/

- Theorem 4 – JC HL The angles in any triangle add to 180° (Angle ABC + Angle BCA + Angle CAB = 180°)

https://www.projectmaths.ie/geogebra/theorem-4/

- Theorem 5. Two lines are parallel if and only if, for any transversal, the corresponding angles are equal.

https://www.projectmaths.ie/geogebra/theorem-5/

- Theorem 6. Each exterior angle of a triangle equals the sum of the interior opposite angles.

https://www.projectmaths.ie/geogebra/theorem-6/

- Theorem 9. In a parallelogram, opposite sides are equal and opposite angles are equal.

https://www.projectmaths.ie/geogebra/theorem-9/

- Theorem 10. The diagonals of a parallelogram bisect each other.

https://www.projectmaths.ie/geogebra/theorem-10/

- Theorem 13. If two triangles are similar then their sides are proportional, in order

https://www.projectmaths.ie/geogebra/theorem-13/

- 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.

https://www.projectmaths.ie/geogebra/theorem-14/

- 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.

https://www.projectmaths.ie/geogebra/theorem-15/

- Theorem 11

https://www.projectmaths.ie/geogebra/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.

https://www.projectmaths.ie/geogebra/theorem-12/

- 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.

https://www.projectmaths.ie/geogebra/theorem-19/

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