Student Activites

Student Activities.

The angle opposite the greater of two sides is greater than the angle opposite the lesser. Conversely, the side opposite the greater of two angles is greater than the side opposite the lesser angle. The lesson begins by looking at an example from real life, using a director’s chair and poses a question which knowledge of the theorem should help to explain. The first part is a practical investigation of the theorem with student activities. Part two leads guides students through a formal proof, requiring students to make deductions using previous theorems and axioms (teacher’s board work is included). Students are now asked to answer the question on the director’s chair again. Part three involves student investigation of the converse of the theorem and part four guides students through a proof of the converse using proof by contradiction.

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Two sides of a triangle are together greater than the third. In this activity student are discovering for themselves that by measuring sides of triangles formed with Geo Strips, two sides of a triangle are together greater than the third.

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Theorem 13

If two triangles are similar, then their sides are proportional, in order. This is a practical introduction to this theorem. It moves from the concrete to the abstract and the student activities verify its claim. The results obtained by the students reinforce the understanding of the properties of similar triangles.

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The Converse of Pythagoras’ Theorem: These activities aim to bring students to an understanding of what the converse of a theorem means and then to investigate whether in fact the converse of Pythagoras holds by investigating a number of triangles formed by Pythagorean triples.

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2. Theorem 21 Leaving Certificate ordinary Level:

(i) The perpendicular from the centre to a chord bisects the chord.
(ii)The perpendicular bisector of a chord passes through the centre.

In this activity the students are guided through a route of discovery to an understanding of both sections of this theorem. After each section the students’ discovery is reinforced.

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3. PowerPoint on circular motion vs. simple harmonic motion (using the London Eye):

PowerPoint showing the relationship between circular motion and the sine function:
Students will use their experiences of circular motion on a Ferris wheel such as the London
Eye, to visualise the change in the y displacement above a horizontal diameter line, as a
point revolves around a circle, thus preparing them for drawing the graph of y= sin x,
referred to in the T&L on trigonometric functions.

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4. Synthetic Geometry : Guide to Axioms, Theorems and Constructions for all Levels.

This document is intended as a quick guide to the various axioms, theorems and constructions as set out in the Appendix to Strand 2 -Geometry and Trigonometry. It is not intended as a replacement for that appendix, merely as an aid to reading at a glance which material is required to be studied at various levels.
As stated in the heading, these theorems and constructions are underpinned by 46 definitions and 20 propositions which are all set out in the appendix, along with many undefined terms and definable terms used without explicit definition.

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