Download Section 2.5 Exploring Congruent Triangles

2.5ExploringCongruentTriangles.notebook
October 30, 2012
Section 2.5
Exploring Congruent Triangles
Goal: Determine the minimum amount of
information needed to prove that two
triangles are congruent.
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Two shapes are congruent if all sides and
angles in one, are equal to the sides and
angles in the other.
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Name the corresponding sides and angles of
the following triangles.
Are the triangles congruent?
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ΔABC ΔPQR
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Identify the congruent parts of the following
triangles.
Write the congruency statement, if possible.
=
=
=
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X is
If I told you that the measure of
65°, and nothing else, is there only
one triangle you could draw?
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If I told you that the length of YZ is
2.74 m, and nothing else, is there only
one triangle you could draw?
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What if I gave you two pieces of
information?
What if I gave you three pieces of
information?
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There are minimum sets of angle and side
measurements that, if known, allow you to
conclude that two triangles are
congruent.
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CONGRUENCE POSTULATES
(SSS) Side - Side - Side Postulate
If the sides of one triangle are congruent to the
sides of a second triangle, then the triangles are
congruent.
SSS EXAMPLES
http://www.mathopenref.com/congruentsss.html
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(SAS) Side - Included Angle - Side Postulate
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another
triangle, then the triangles are congruent. The included
angle is the one that is between the two known sides.
SAS EXAMPLES
http://www.mathopenref.com/congruentsas.html
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(ASA) Angle - Included Side - Angle Postulate
If two angles and the included side of one triangle are
congruent to two angles and the included side of another
triangle, then the triangles are congruent.
http://www.mathopenref.com/congruentasa.html
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(AAS) Angle - Angle - Not Included Side Postulate
If two angles and the non-included side of one triangle
are congruent to two angles and the non-included side
of another triangle, then the triangles are congruent.
http://www.mathopenref.com/congruentaas.html
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Congruent Triangles - Why SSA doesn't work
http://www.mathopenref.com/congruentssa.html
Congruent Triangles - Why AAA doesn't work
http://www.mathopenref.com/congruentaaa.html
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Are the following triangles
congruent? Why or why not?
If the triangles are congruent, state
the congruence statement.
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Are the following triangles
congruent? Why or why not?
If the triangles are congruent, state
the congruence statement.
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Are the following triangles
congruent? Why or why not?
If the triangles are congruent, state
the congruence statement.
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If the triangles are congruent, state
the congruence statement.
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2.5 Assignment: Nelson Foundations of Mathematics 11, Sec 2.5, pg, 106
Questions: 1 ‐ 4
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