The Standard Deviants show you what makes isosceles and right triangles special, as well as polygons and quadrilaterals.
Subjects: Geometry
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The Pythagorean Theorem
It’s geometry in the real world, then a visit to triangle court to prove a few theorems about right triangles. Afterwards, the Standard Deviants introduce the Pythagorean theorem, one of the most famous theorems in geometry, and two special types of right triangles.
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Similarity, Ratio and Proportion
This program presents the ideas of similarity, ratio and proportion in a refreshing and informal style. Examples are drawn from everyday life using familiar objects with on-screen graphics producing clear well defined diagrams. Thorough explanations are provided with worked examples and student practice is also included. Methods to obtain indirect measurements are simplified and elegantly demonstrated, including surveying methods to find the width of a river and a mirror to find the height of a tall object. Both of these methods are suitable for student activities and use readily obtainable equipment.
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Coordinate Geometry
The program explores the first quadrant of the Cartesian plane in the context of a city street grid, then looks at using coordinates, graphing relationships and how slope is measured.
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Geometric Transformations
The program uses everyday situations and examples to explain the major types of geometric transformations: translations, rotations, reflections and dilations
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Naming and Measuring Angles
This program provides students with a lively introduction to key concepts involved with angles, such as how we define and write information about an angle, mathematical notation for rays, line segments and lines, and how to use a protractor. Obtuse and acute angles are illustrated, the relationships between the angles formed by a transversal crossing parallel lines are investigated and congruent triangles are introduced, all using examples from real life, supplemented by clear graphic overlays and simple animations.
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Geometric Constructions
The program demonstrates the following constructions in the context of a student creating a mobile to hang above a baby’s cot: Bisecting an angle; Perpendicular bisector of a line; Constructing a triangle using three known side length; Determine the center of gravity by constructing medians; Determine the inscribed circle of a triangle by constructing the angle bisectors; Determine the circumcircle of a triangle by constructing the perpendicular bisectors.
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Triangles and Quadrilaterals
The program explains how triangles can be classified by side length and by angles, introducing the mathematical names. It then names and illustrates the different types of convex quadrilaterals.