Text Set #1: Triangle Congruence

Books/Print Resources

·      Geometry Workbook For Dummies

Mark Ryan

Grade level: 12 (for teachers to use in instruction)

This book has a good ‘plain language’ approach to geometry, though the reading level is a bit high.  I would certainly use it sparingly, and mostly on concepts that don’t have much in the way of an access point for students.  Some of the exercises are also presented well and broken down into small steps and would be appropriate for students who get overwhelmed by multi-step problems. 

·      “The History and Concept of Mathematical Proof”

Steven G. Krantz

Accessed from http://www.math.wustl.edu/~sk/eolss.pdf

Grade level: 8.6

This text might be nice for advancing students who perform highly and need activities that deepen their understanding of geometry, but section 4 on the history of geometry would be a good assignment for the whole class. It could even be a read-along for those classes that struggle with reading. 

Activities/Websites

·      Triangle Congruency By SSS and Properties of Isosceles Triangles Activity

http://education.ti.com/en/us/activity/detail?id=486E4EB82B77484BBC4C0097DF3FE3E1

Grade level: 6.6

This is a great in-depth application lesson on using triangle congruency and the properties of isosceles triangles.  The lesson includes an authentic problem about building a doghouse, and set ups for analysis based on symbolic, graphic, and verbal representations.  I find this activity useful because of the depth and variety of representations in analysis. 

·      Conditions That Prove Congruency

http://education.ti.com/en/us/activity/detail?id=359A3010A7CE45C89995C27ABEC063CB

Grade level: 7.7 and above

 This activity combines conceptual and abstract verbal representations with interactive portions that let students determine empirically the conditions necessary to prove congruence in triangles.  It lets students see first-hand how changing various parts of a triangle affects congruence. 

·      Math for Morons Like Us

http://library.thinkquest.org/20991/geo/ctri.html

Grade level: 10.1

This page is a good reference for the five triangle congruence theorems, and provides great examples of small, manageable proofs for each of the cases.  It also has a little quiz at the end to test student knowledge.

·      Regents Prep: Practice with Proofs Involving Congruent Triangles

http://www.regentsprep.org/Regents/math/geometry/GP4/PracCongTri.htm

Grade level:  8.3

This activity gives good triangle congruence proofs for increasingly complex figures.  It uses the ‘traditional’ two-column form used in Geometry classes, and challenges students to try the proof before clicking to reveal the answer. 

·      Khan Academy: Congruent Triangles

https://www.khanacademy.org/math/geometry/congruent-triangles

Grade level: 11.9

Khan Academy’s collections on triangle congruency combine visual/symbolic representations with aural presentations.  It is good for those students who favor auditory methods and who may get ahead of themselves with verbal representations, thus losing the sequential logic of the proof.  Of course, after the videos, Khan Academy has some stellar interactive quiz questions.

·      Khan Academy: Congruence, Isosceles and Equilateral Triangles

https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/geometry_proofs_intro

Grade level: 8.8

See previous entry on rationale for videos; proof questions here are constructed as a fill in the blank for parts of the triangle with a drop-down box supplying the properties to be used as justification. 

·      Wikipedia: Congruence (geometry)

http://en.wikipedia.org/wiki/Congruence_(geometry)

Grade level: 12

Honestly, Wikipedia is actually usually a pretty good place for establishing a baseline for a mathematical concept.  Now, I wouldn’t have have the students read the entire page because it gets technical, but the intro and selected sections are good, as are the .gifs in the sidebar. 

·      WyzAnt Resources: Congruent Triangles

http://www.wyzant.com/resources/lessons/math/geometry/triangles/congruent_triangles

Grade: 10.7

This webpage uses a nice, approachable conversational tone to discuss congruence, primarily in a verbal mode.   Also, the figures here are understandable and clearly marked with different colors to indicate congruent parts. 

·      Regents Prep: Lesson on Theorems for Congruent Triangles

http://www.regentsprep.org/Regents/math/geometry/GP4/Ltriangles.htm

Grade level:  9.3

The first part of this page is nothing special and is a less stellar version of some of the other resources I’ve included in this set, but the last third of the page is dedicated to a discussion on why AAA and ASS are not valid as congruency postulates.

·      Math is Fun: Congruent Triangles

http://www.mathsisfun.com/geometry/triangles-congruent.html

Grade level: 5.8

This would be a good resource for students who do not read at a high school level.  It is simple introduction to congruence with simple figures – nothing overly complicated. 

·      Math Warehouse: Isosceles Triangle Theorems and Proofs

http://www.mathwarehouse.com/geometry/congruent_triangles/isosceles-triangle-theorems-proofs.php

Grade level: 6.7

This site is good to look at proofs in an incremental fashion, if it is a bit garish. 

·      Geometry History

http://www.kidsmathgamesonline.com/facts/geometry/history.html

Grade level: 12.0

Despite having a Flech-Kinkaid level of 12, this page provides a few basic historical facts about Geometry and geometric constructions.  I’m not entirely convinced that the reading level is as listed – I think the Greek root words discussed skew the measure.

·      Math Open Reference: Introduction to Constructions

http://www.mathopenref.com/constructions.html

Grade level: 7.9

This site gives a little bit of background on construction proofs and provides a nice answer for that student who always says “Well why didn’t they just measure it?”  It also has a collection of links to pages on constructions and proofs.