Download Criteria for Triangle Congruence Solutions

Solutions to Stations Resource
*Station One- Given AB  14.7 cm, AC  18 cm, and  A  34 
Students will create different options for a triangle with these parameters, but will
discover that only identical triangles will result. Triangles may be transformed
(translated, rotated, reflected), but all triangles will be congruent. Students will form the
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conjecture that if two sides and the angle between them (included angle) in one triangle
are congruent to two sides and the included angle in another triangle, then the triangles
are congruent. (SAS Congruence)
*Station Two- Given  A  34 , AB  14.7 cm, and  B  92 
Students will create different options for a triangle with these parameters, but will
discover that only identical triangles will result. Triangles may be transformed
(translated, rotated, reflected), but all triangles will be congruent. Students will form the
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conjecture that if two angles and the side between them (included side) in one triangle are
congruent to two angles and the included side in another triangle, then the triangles are
congruent. (ASA Congruence)
*Station Three- Given AB  14.7 cm,  B  92 , and  C  54 
Students will create different options for a triangle with these parameters, but will
discover that only identical triangles will result. Triangles may be transformed
(translated, rotated, reflected), but all triangles will be congruent. Students will form the
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conjecture that if two angles and the side not between them (non-included side) in one
triangle are congruent to two angles and the corresponding side not between them in
another triangle, then the triangles are congruent. (SAA Congruence)
*Station Four- Given  A  34 ,  B  92 , and  C  54 
Students will create different options for a triangle with these parameters and will
discover it is possible for non-congruent triangles to result. Triangles will always be
similar to each other (same shape), however students will create triangles of varying
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sizes. Students will form the conjecture that if three angles in one triangle are congruent
to three angles in another triangle, then the triangles are not necessarily congruent.
(AAA)
*Station Five- Given AB  14.7 cm, AC  18 cm, and BC  10 cm
Students will create different options for a triangle with these parameters, but will
discover that only identical triangles will result. Triangles may be transformed
(translated, rotated, reflected), but all triangles will be congruent. Students will form the
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conjecture that if three sides of one triangle are congruent to three sides of another
triangle, then the triangles are congruent. (SSS Congruence)
*Station Six- Given AB  14.7 cm, AC  18 cm, and  C  54 
Students will create different options for a triangle with these parameters and will
discover it is possible for non-congruent triangles to result. Students will form the
conjecture that if two sides and an angle that is not included in one triangle are congruent
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to the corresponding two sides and an angle that is not included in another triangle, then
the two triangles are not necessarily congruent. (SSA)
1. Which stations resulted in the creation of at least one triangle of a different size or
shape while still utilizing the given criteria?
 Stations four and six
2. Which stations resulted in the creation of all identical triangles no matter how
many different ways you put together the given dimensions and/or angle
measures?
 Stations one, two, three, and five