SOLUTION: Which of the following conditions cannot be used for checking that two triangle are congruent? (1) two corresponding angles and corresponding sides are equal (2) two correspondin

Algebra ->  Geometry-proofs -> SOLUTION: Which of the following conditions cannot be used for checking that two triangle are congruent? (1) two corresponding angles and corresponding sides are equal (2) two correspondin      Log On


   

Question 499186: Which of the following conditions cannot be used for checking that two triangle are congruent?
(1) two corresponding angles and corresponding sides are equal
(2) two corresponding sides and the corresponding included angles are equal
(3) three corresponding angles are equal
(4) three corresponding sides are equal
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Use the process of elimination.
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Which of the following conditions cannot be used for checking that two triangle are congruent?
(1) two corresponding angles and corresponding sides are equal
(2) two corresponding sides and the corresponding included angles are equal
(3) three corresponding angles are equal
(4) three corresponding sides are equal
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(1) Clearly this will work because with 2 angles and 2 sides, there is no freedom for the third side. The third angle has to be 180 - sum of the 2 sides. The third side has to be fixed.
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(2) This will work, too. The third angle is defined by knowing the two angles. The third side of the triangle is defined precisely and has not freedom to vary.
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(3) This will not work. The triangles will be similar if all three angles are equal. But one could be microscopic and the other could be the drawn on a football field.
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(4) This works. If the sides are all the same length, then the angles will be the same.
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Question: Which will not work? (3) will not work.