Congruent Triangles
I. Discover "What is a Proof"!
a. Read over "What is a Proof?"
http://www.regentsprep.org/Regents/math/geometry/GP3/WhatPrf.HTM and study who is
responsible for them, and the best strategy for completing proofs.
b. Read Section 2.1 - Proofs http://en.wikibooks.org/wiki/Geometry/Chapter_2 from Wikibooks.
c. Thoroughly read the history of proofs
http://www2.andrews.edu/~calkins/math/webtexts/geom05.htm#HIST.
II. What is Congruence?
a. Study each of the following the definitions of congruence. Create a definition, in your own
words, for congruence. Record this in your notes and with the teacher.
1. Merriam-Webster Dictionary http://www.merriam-webster.com/dictionary/congruent
2. Dictionary.com http://dictionary.reference.com/browse/congruent
b. How is it possible to have congruent figures
http://www.math.com/school/subject3/lessons/S3U3L1GL.html? Read steps 1 through 4, but make
III. How do we prove Triangles Congruent?
Read through each of the different explanations of how triangles can be proven to be congruent.
Take any supplementary notes you need and add them to your notebook.
1. AnalyzeMath.com http://www.analyzemath.com/Geometry/congruent_triangles.html
2. Math For Us
a. SAS http://library.thinkquest.org/20991/geo/ctri.html#SAS
b. SSS http://library.thinkquest.org/20991/geo/ctri.html#SSS
c. ASA http://library.thinkquest.org/20991/geo/ctri.html#ASA
d. AAS http://library.thinkquest.org/20991/geo/ctri.html#AAS
IV. Time to Practice!!
Try each of the activities at the following websites. Make sure to follow directions, and
turn in to the teacher all requirements.
1. From EdHelper.com http://www.edhelper.com/math/geometry_congruent_triangles2.htm
print off this page, complete the problems, and turn in to the teacher for review and
feedback.
2. Complete all of the examples from the Recognizing Congruent
Triangles http://www.regentsprep.org/Regents/math/geometry/GP4/BegTriPrf.htmactivity.
Make sure to try the interactive matching game
http://www.regentsprep.org/Regents/math/geometry/GP4/matchingpartsgame.htm . Make a tipsheet from the tips provided at this site and keep it in your notebook plus check them
with the teacher. See rubric for grading.
3. Use this interactive proof practice
http://www.regentsprep.org/regents/math/geometry/GP4/preprooftriangles.htm to strengthen
your concepts of congruent triangles.
VI. CPCTC: What is it? How is it used?
1. Use a search engine such as Google or Mamma to find out:
a. What does CPCTC stand for?
b. When is it used in a proof?
Turn your written answers in to the teacher for review and feedback.
2. Now that you know what CPCTC is for, check it out in action!
http://library.thinkquest.org/20991/geo/ctri.html#CPCTC
V. Complete the Congruent Triangles Project for evaluation. Make sure to
follow directions and meet all criteria as described in the rubric in the
evaluation section.
Objective: Explain and demonstrate the 5 different reasons why triangles can be
congruent. Include diagrams, what a two-column proof is with examples of triangle
proofs, a brief history on two-column proofs in geometry. Lastly, demonstrate CPCTC's
use in two-column proofs involving triangles.
Chose one of the following for your project
Congruent
Triangles
Project
Write a 3-5 page paper with
images, diagrams, and
examples with references
cited properly (APA format).
Create a children's book . Create a PowerPoint
centered
presentation that contains
around proving
links to websites and images.
triangles congruent.
Last slide should be a
reference page.
Evaluation
A
B
C
D
E
Task 1
10
8
6
4
2 or below
What is a proof
Well done
notes on all
three sites
Ok notes on all
3 sites
Notes on two
sites
Notes on one
site
Notes on no
sites
Task 2
10
8
6
4
2 or below
Definitions
Went to each
site and wrote
a definition
Went to each
site
Went to some
of the sites
wrote a
definition
Went to some
of the sites
Didn’t go to
any of the sites
Task 3
10
8
6
4
2 or below
Notes on
congruence
Wrote notes
on all 5 sites
Write notes on
4 of the sites
Wrote notes
on 3 of the
sites
Wrote notes
on 2 of the
sites
Did nothing
Task 4
20
16
14
12
11 or below
CPCTC
Looked up
what it meant
and wrote
notes on
lesson
Wrote notes
on lesson
Looked up
what it ment
Did a little of it
Did nothing
Task 5
50
40
35
30
29 or below
Project
Demonstrated
a full
understand of
triangles
Demonstrated
understanding
about some of
congruence
Very few
understanding
of congruence
Almost no
understanding
No project