# GeoGebra

GeoGebra is free and multi-platform dynamic mathematics software for learning and teaching. It has received several educational software awards in Europe and the USA.

• #### Simultaneous Equations 2

This GeoGebra applet is similar to Simultaneous Equations 1 but with this applet up to 5 of the variables can be changed. As with the other, the answer and working can be displayed. While the first applet could be used more for the elimination method of solving simultaneous equations, this could be used to show the substitution method of solving simulataneous equations. Year / Level: Year 10+
• #### Triangle Angles

This simple applet illustrates two aspects of triangles, the first being that the internal angles add to 180 degrees and the second that the exterior angle of a triangle sums to the total of the two opposite interior angles. A final observation is that the external angle and the adjacent internal angle are both on a straight line and therefore sum to 180 degrees as well. By moving around point C students will easily comprehend this easy concept. Year / Level: Year 9
• #### Right Angle Triangles

This applet has multiple features and requires a little bit of time to play with it to see the possibilities. Teachers can use it in the computer lab with students working through a check list (see the Right Angle Record Sheet PDF file provided). The big idea is that you select what to hide and what to show, move the "find" word to a chosen side or angle. Then select the formulae SOH CAH TOA or Pythag, hiding the ones not required. Move the labels to the correct position, (in the case of SOH CAH TOA, after labels are in place the formulaes not required are hiden also) and make the correct calculations. Students use their normal calculator for this, but if they do not have one use an online one. Calculations are checked by displaying the side or angle you have calculated. There can be minor rounding errors. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### Right Angle Triangles Record Sheet

This record sheet goes with the Right Angled Triangle Students use their normal calculator for calculations and record on this sheet. Their calculations can then be checked by displaying the side or angle you have calculated. There can be minor rounding errors. This PDF file  was supplied by Priscilla Allan, Pakuranga College.
• #### Trigonometry Cosine Rule

This Geogebra applet allows teachers to demonstrate the Cosine Rule for non-right angled triangles. Move any of the triangles vertices around and observe how the angles and sides change. Students need to use a calculator and the Cosine Formula to calculate the size of the missing angle. Note that this applet only calculates missing sides. Year / Level: Year 12
• #### Trigonometry Sine Rule

In this GeoGebra Applet the Sine Rule is illustrated. Teachers can choose to show all 3 sides and all 3 angles or partial sides and angles. Students should calculate the missing sides and angles with a calculator and then check their answers with this program. Year / Level: Year 12
• #### Looking at Parabolas

This GeoGebra applet was taken off the GeoGebra New Zealand wiki site. It illustrates all sorts parabola examples in real life such as motorcycle riders and skier jumps, throwing balls and differnent building arches. You can then illustrate that each of these parabolas can actually have an equation added to it. This can be quite handy if doing a motorcycle jump and trying to calculate whether you will actually make it to the ramp on the other side! Year / Level: Year 11+
• #### More Parabolas

In this GeoGebra applet you can use sliders to illustrate y = ax2 + bx + c. The equation can be shown in factorised form or as a product of two squares. The graph can show the x and y intercepts and the vertex. If students want to graph their own equation then on the right hand side of the applet is a handy x, y table.  Year / Level: Year 11+

• #### Explaining Parabolas

This GeoGebra applet shows how the parabola graph relates to the equation in normal and factorised form. It can also be used to illustrate how the axes intersects are related to the equation and how the vertex can then be calculated. Year / Level: Year 11+
• #### Parabolas

This applet provides a visual understanding of the completed square form of the quadratic form
y = a(x - b) + c where a is the shape and (b,c) is the vertex. The equation of the graph, and the vertex can be hidden. Sliders are used for a,b and c. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+