TRIANGLE CONGRUENCE: An Online Treasure Hunt for 3rd Year High School (Mathematics)
Authored by A. Valenzona and P. Arinto
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).
- Do you have to measure all angles and all sides to know that two triangles
are congruent? Explain your answer.
- Triangle LMN is congruent to triangle OPS. Is it correct to say that
triangle LMN is congruent to triangle SOP? Why or why not?
- 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.
- Write in symbols the statement that triangles JKI and QRS are congruent.
- Are two similar triangles congruent? Explain or illustrate your answer.
- What is the meaning of CPCTC?
- Why does the SSA postulate work only with the right triangle?
- Is it possible for two triangles to have equal angles but not equal sides?
Explain or illustrate your answer.
- 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?
Congruence and Triangles
A Summary of Triangle Congruence
Triangle Congruences. Not!
Congruence of Right Triangles
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.