Download Congruent Triangle Postulate Discovery

Name
Date:
Congruent Triangles Postulate Discovery
M05
Communication
-Communicate
math topics using
tables, graphs,
diagrams, symbols,
and math
vocabulary
1
2
3
4
5
-Underline
important
information
-Explain math
ideas verbally
and in writing
using diagrams,
tables, graphs
and symbols.
-Create
mathematical
theories based
on given
information.
-Use different
communication
strategies to
express the
same math idea.
-Communicate
math ideas to
compare or
defend results.
-Write given
information
You are a mathematician trying to disprove or agree with any of the statements below. If it cannot be disproven
then it is a postulate. In order to disprove a statement you must draw the triangle so that it meets all the criteria
listed but forms a different triangle. If you can draw a different triangle then write “Not Always True” on top
of the triangle. If you cannot draw a different triangle then write “Always True” on top of your identical
triangle. Use the protractors and ruler to take accurate measurements.
1) Write in complete sentences what will be expected of you in order to complete this assignment.
AAA Postulate: Two triangles that share three
pairs of congruent angles are congruent.
ASA Postulate: Two triangles that share a pair
of congruent sides in between two pairs of
congruent angles are congruent.
AAS Postulate: Two triangles that share two
pairs of congruent angles that follow one pair of
congruent sides are congruent.
mABC = 53.13
mBCA = 36.87
B
m BA = 3.00 cm
C
A
SSA Postulate: Two triangles that share two
pairs of congruent sides followed by one pair of
congruent angles are congruent.
SAS Postulate: Two triangles that share a pair of
congruent angles in between two pairs of
congruent sides are congruent.
SSS Postulate: Two triangles that share three
pairs of congruent sides are congruent.
HL Postulate: Two right triangles that share a
pair of congruent legs and a pair of congruent
hypotenuses are congruent.
W
m UV = 3.00 cm
m WU = 5.00 cm
V
U
2) Examine the triangles that could not be drawn any differently. Explain the reasoning why those
triangles are constrained (forced to look one way.)
3) Examine the triangles that could be drawn differently. Write the reasons why you were able to
draw different triangles in order to prove that the particular Postulate does not exist for each
disproven triangle theorem.
4) Prove your same theories from question 3 through illustration. Create triangles with different
measurements and see if your statement holds true.
5) Defend the postulates you proven to be “always true” by explaining in complete sentences why
they are always true.