Mystery Transformations

In each mystery you are given two triangles that are related by a function belonging to one of five function families: rotate, reflect, translate, glide reflect, or dilate. Your task is use one of the tools to construct an image of `triABC` and then adjust your function (by adjusting the center, mirror, vector, angle, of scale factor) to demonstrate that the two triangles are congruent or similar.

**Mystery 1:** Each page tells you what function family to use. Your task is to apply that function to `triABC` and then adjust your function so that `triA'B'C'` lies directly on top of `triDEF`.

**Mystery 2:** On each page you have to decide which function family to use before you apply your function to `triABC` and adjust it to superpose `triA'B'C'` on `triDEF`.

**Mystery 3:** The function tools give you only an independent and dependent variable. On each page you have to choose the function family, restrict `x` to `triABC` as its domain, and adjust your function so that the range is `triDEF`.

1 Mystery 1: Demonstrate Congruence or Similarity

On each page, use a different transformations to superpose an image of `triABC` on `triDEF`.

You can use the designated transformation tool and adjust the function rule to superpose the two triangles. You may find the construction tools useful in this process.

Press the New Case button for a new `triABC` and a new function rule (still using the same function family).

How can the construction tools make it easier to solve new cases?

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2 Mystery 2: Choose the Function

On each page, you must first figure out what transformation connects the two triangles.

Then perform the necessary construction to superpose an image of `triABC` on `triDEF`.

Record the features you used, on each page, to identify the correct function to use.

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3 Mystery 3: Match the Domain and Range

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4 Objectives

As you perform the activities in this lesson, you will:

- Apply transformations to triangles.
- Use transformations to superpose one triangle on another, experimenting with the function rule to make them fit exactly.
- Determine which transformations are isometries; that is, which preserve distances.
- Describe the meaning of “superpose” and “superposition” in your own words.
- Given two triangles, identify which transformation allows you to superpose one on the other.
- Describe transforming one point to another is related to transforming one triangle to another.

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:**

21 July 2018: Created this page.