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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 11 – 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-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 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: 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 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!