It is one thing to find the solution with pencil and paper, it then becomes entirely another thing to reproduce the shapes with transformations, thus taking the challenge on to another level.įinding centres of rotation is probably the trickiest element and this exercise really helps students to think about and explore this idea. From my experience, students believe they can separate the shapes according to the rules and want to have a go.Īs the exercise progresses, it becomes apparent that in some cases there is more than one solution and that in others, the solution requires a bit of lateral thought. In the beginning there is an element of puzzle solving that is engaging. I am often inspired by the notion that 'Opportunties to practise can be found inside rich tasks'. This is just a quick summary of why I think this is such a rich classroom activity. (This screen cast was made using autograph software, but it could easily be done in any dynamic geometry software) See the eample below.Īnd see more examples of how to do it in this video that explains and outlines the task. You will know when you have done it because your two shapes together will make the original shape you staretd with. You will need to create and use mirror lines, centres of rotation and translation vectors and get the size and positions correct. You need some real lateral thought to figure out how to divide the shapes in two such that both of the halves are congruent shapes! What is different about this activity, is that you are being asked not only to solve this bit of the problem, but to construct these shapes using technology and by drawing half of the shape and transforming it to create the other half! This will involve reflection, rotation, translation and maybe some combinations of the three. These problems are brilliant and have been around for ages. If one shape can become another using Turns, Flips and/or Slides, then the shapes are Congruent: Rotation: Turn Reflection: Flip Translation: Slide After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths. 'Can you cut these shapes in 2 such that the two halves are congruent?' Geogebra(advanced):Create your own Interactive materials.To summarize, congruent figures are identical in size and shape the side lengths and angles are the same. Applications, Hands-on Maths & Self-instruction Here are two congruent figures with an example of one rotated, one translated up, and one reflected (flipped): Congruent shapes example - asymmetrical figures reflection.Logarithms: What are they? History & Applications.IBDP Maths: Applications & Interpretation.
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