Lesson Activities on Geometry Proofs
Geometry is a branch of mathematics that deals, in part, with the laws and properties of physical space. Among other things, geometrical proofs attempt to explain the relationship between shapes, angles and lines. While learning geometry proofs, there are many lesson activities in which students can take part. The most effective of these activities are those that appeal to multiple learning styles simultaneously.
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Proofs and Shapes
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In an effort to simultaneously visualize and understand how proofs apply to different geometric shapes, students can work through and complete different proofs and then check their answers against the reality of a cut-out of a geometric shape. For example, to demonstrate the veracity of the congruency proof regarding isosceles triangles, students can examine several examples before solving the proof. Upon solving the proof, they can measure both the sides and angles of a cut-out of an isosceles triangle with congruent sides and determine if the angles opposite each congruent side are also themselves congruent.
Proofs and Origami
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Similar to working with cut-outs of shapes about which geometric proofs can be written, working with proofs and the paper-folding technique known as origami will allow students to apply theoretical principles to concrete, manipulable examples. In working with origami, students can examine a proof before attempting to prove its veracity by folding pieces of paper. For example, in order to prove the proof that a perfect square is comprised of two congruent right triangles, students can simply measure a piece of square origami paper in half.
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Proofs and Graphic Organizers
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So as to organize geometric proofs, as well as demonstrate how different proofs work in similar ways, students can create a graphic organizer to organize proofs according to their different components. For example, a graphic organizer for some simple proofs might include a column dedicated to the statements of the proofs, another for the reason for the proof and a third for a diagram or physical demonstration of the proof.
Geometrical Concepts
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As geometric proofs are mathematical demonstrations of inductive and deductive logic, students who are more auditory learners may benefit from simple analyses of the basic geometrical concepts that yield geometric proofs. For example, students might analyze the symbolic equations that yield certain proofs and attempt to identify logical validity and soundness, as well as inductive implication.
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References
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