Triangle Congruence

Introduction

Hello everyone, we will be learning the criteria necessary to determine if two triangles are congruent. Before we explore the nature of triangle congruence, we will revisit the distinctions between congruence and similarity in some detail. Below I have attached a visual representation of such distinctions:

TingMath - What are similar vs congruent shapes? Similar shapes are shapes that are stretched proportionally to a factor, while congruent triangles are exactly the same shape and size #math #emath #olevelmath #

Task

When we finish exploring the nature of triangle congruency, you will be tasked to create a mind map on a paper that will support your thinking process. In addition, you will be tasked to explain the concept of triangle congruence to a partner. After this, each group will concisely explain some aspects of triangle congruence on the board without using too many words. Finally, you will be assigned a  quizizz to assess your knowledge with at least ten questions. I have attached supplemental resources to guide you on this endeavor. Also, I have attached a visual representation of a mind map for your reference below:

What is a Mind Map? | MindMapping.com

Process

For each individual, I would suggest the following steps necessary to complete this task:

  1. Review this video on creating mind maps for beginners: 

    1. https://www.youtube.com/watch?v=gLHqVR6VDUg&authuser=0

  2. Read Chapter 4: Triangles-Basic  (pg.29-37) and review this video elaborating on the topic:
    1. https://www.youtube.com/watch?v=jWHOF6cFbpw&authuser=0
    2. https://mathguy.us/Handbooks/GeometryHandbook.pdf
  3. Create a mind map that illustrates your thinking process.
  4. After the group presentation, complete the following quiz:
    1. file:///C:/Users/16622/Downloads/4-Congruence%20and%20Triangles.pdf
Evaluation

 

Rubric for Mind Map:

Degree of Relevance Scores
Related   100 Corresponds to the topic at hand
Somewhat Related 75 Closely corresponds to the topic at hand
Not Related 25 Does not correspond to the topic at hand

 

The test will be graded according to a 10 point scale with 100 being the max score.

 

 

 

Conclusion

For this web quest, students were tasked to create a mind map and collaborate with a partner. Finally, students were given a quiz to test their knowledge.

Credits
Teacher Page

In this WebQuest, I have provided students with educational resources to help consolidate their knowledge of triangle congruency. Below are the standards given by the 2016 Mississippi College- and Career Readiness Standards for Mathematics that correspond to the information provided above:

  1. G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor:
    1.  A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
    2.  The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
  2. G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  3. G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
  4. G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.