TRIANGLE CONGRUENCE

An Online Treasure Hunt
For Third Year High School (Mathematics)

 
Introduction

Two triangles are congruent. Does this mean they are equal? Two triangles are similar. Does this mean they are congruent?

In this lesson, you will be introduced to triangle congruence. The lesson is in the form of a game, an online treasure hunt. You are given a series of questions below. The answers to these questions (or the “treasures”) can be found in the websites listed. Read each website carefully to find the answers you seek.

You will work on the treasure hunt in groups of three. That’s a number that is very apt for our lesson today: The prefix “tri” in the word “triangle” means three—there are three sides to a triangle as well as three angles! Do work together and help each other understand the lesson on triangle congruence. One way of making sure that each member participates in the activity is to have each member take the lead in answering three questions (there are nine question in all). This does not mean that the other two members will not help the third member answer the questions assigned to him/her. Remember that you are expected to submit one set of answers and that you will be graded as a group.

After answering the questions, proceed to the Big Question.

Write all answers neatly on a sheet of paper. Remember to write the names of all group members as well. You have one hour to complete this activity (including answering the Big Question).

Questions
  1. Do you have to measure all angles and all sides to know that two triangles are congruent? Explain your answer.

  2. Triangle LMN is congruent to triangle OPS. Is it correct to say that triangle LMN is congruent to triangle SOP? Why or why not?

  3. The SSS, ASA, and SAA postulates together signify what conditions must be present for two triangles to be congruent. Do all of the conditions these postulates represent together have to be present for two triangles to be congruent? Explain briefly.

  4. Write in symbols the statement that triangles JKI and QRS are congruent.

  5. Are two similar triangles congruent? Explain or illustrate your answer.

  6. What is the meaning of CPCTC?

  7. Why does the SSA postulate work only with the right triangle?

  8. Is it possible for two triangles to have equal angles but not equal sides? Explain or illustrate your answer.

  9. In triangle ABC, AB = 12, BC = 12, and angle b = 45°.  In triangle XYZ, XY = 12, YZ = 12, and angle y = 45°.  Are the triangles congruent?

Resources

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

Similar Triangles
http://argyll.epsb.ca/jreed/math9/strand3/triangle_congruent.htm

Congruence and Triangles
http://mathforum.org/library/drmath/view/54673.html

A Summary of Triangle Congruence
http://www.math.washington.edu/~king/coursedir/m444a03/notes/congruence%20html/tri-congruence-summ.html

Triangle Congruence
http://mathforum.org/library/drmath/view/62849.html

Triangle Congruences. Not!
http://www.andrews.edu/~calkins/math/webtexts/geom07.htm

Congruence of Right Triangles
http://www.e-zgeometry.com/class/class5/5.2/5.2.htm

The Big Question

If you knew only two measures each of two triangles, would you be able to tell that the two triangles are congruent? Explain your answer.


Authored by A. Valenzona and P. Arinto