The SSS Theorem

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.)

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.

3 Superposition by a Single Transformation

In this sketch you’ll use a single transformation to show superposition for any pair of congruent triangles.

4 Construct the Superposition

In this sketch you’ll *construct* a single transformation to show superposition for any pair of congruent triangles.

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**

Release: 2015Q4Update2, Semantic Version: 4.5.1-alpha, Build Number: 1026.6-wsp-widgets, Build Stamp: stek-macbook-pro/20180605163618

Web Sketchpad Copyright © 2017 KCP Technologies, a McGraw-Hill Education Company.

“You may freely use Web Sketchpad in your own Web pages, provided you do so for non-commercial use only” [per kcpt.github.io].

“You may freely use Web Sketchpad in your own Web pages, provided you do so for non-commercial use only” [per kcpt.github.io].

License: Creative Commons CC-BY-NC-SA 4.0

**Update History:**

24 Oct 2017: Created this page.