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An investigator at a crime scene found a triangular piece of torn fabric. The investigator remembered that one of the suspects had a triangular hole in their coat. Perhaps it was a match. Unfortunately, to avoid tampering with evidence, the investigator did not want to touch the fabric and could not fit it to the coat directly.
a) If the investigator measures all three side lengths of the fabric and the hole, can the investigator make a conclusion about whether or not the hole could have been filled by the fabric?
b) If the investigator measures two sides of the fabric and the included angle and then measures two sides of the hole and the included angle can he determine if it is a match? Explain.

Sagot :

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Answer:

  a) yes

  b) yes

Step-by-step explanation:

a) Triangles can be proven congruent by the SSS postulate, so knowing the three side lengths is sufficient to demonstrate the piece will fit in the hole.

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b) A triangle can be solved (completely specified) if two sides and the included angle are known. Those measurements on the fabric and the hole allow all side lengths and angles of the triangles to be determined completely. Hence the triangles can be shown congruent as a result.

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Additional comment

Showing SSS congruence generally means demonstrating corresponding sides are the same length. However, the three side lengths completely specify the triangle. The side lengths can always be made corresponding if they are listed in some order, for example, shortest to longest.

Showing SAS congruence requires that corresponding sides and angles be shown congruent. However, an SAS specification of a triangle is sufficient to permit determination of all sides and angles. Specifically, the third side length can be found using the Law of Cosines, and the remaining angles can be found from either the Law of Sines or the Law of Cosines.

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