In this lesson you'll investigate whether having the three sides of one triangle equal in length to the three sides of another triangle means that the two triangles must be congruent. If this is true, there must be a rigid motion (a transformation) that superposes the image of one triangle on the other triangle, and your task will be to do the construction and describe your strategy. If this is false, your task will be to construct a counter-example.
In the first websketch you’ll use SSS to construct some triangles.
1 What is SSS?
SSS stands for “Side-Side-Side” and refers to a pair of triangles in which the three sides of one triangle are exactly the same lengths as the three sides of the other triangle.
- On page 1 you’ll construct a triangle using the lengths of the three given segments.
- On page 2 you’ll construct two triangles of different orientation using the side lengths of the given triangle.
(Two triangles have the same orientation if the corresponding sides in the triangles are arranged both in clockwise order or both in counterclockwise order. Two triangles have different orientation if the corresponding sides are in clockwise order in one triangle, but in counter-clockwise order in the other.)
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2 SSS Superposition by Adjustment
On each page, use the reflect function to superpose the image of `triABC` on `triDEF`. Some pages will require you to use the reflect function more than once.
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3 Superposition by a Single Transformation
In this sketch you’ll use a single transformation to show superposition for any pair of congruent triangles.
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4 Construct the Superposition
In this sketch you’ll construct a single transformation to show superposition for any pair of congruent triangles.
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5 The Fine Print
Requirements:
These activities require web access using a browser that supports HTML5 and JavaScript. (That means almost any current browser.) No purchase is required, and there’s no advertising anywhere.
Release Information
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This web site is based in part upon work supported by the National Science Foundation under NCSU IUSE award 1712280 (July 2017 through December 2020) and KCP Technologies DRK-12 award ID 0918733 (September 2009 through August 2013). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
We are deeply grateful to McGraw-Hill Education
for making Web Sketchpad available for these lessons.
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