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What information is necessary to prove two triangles are similar by the SAS similarity theorem?



Provide an example of two triangles you could show are similar using the SAS similarity theorem.

Answer :

Final answer:

To prove two triangles are similar by the SAS similarity theorem, two sides must be in proportion and the included angle must be equal. For example, if Triangle A has sides of 6 cm and 8 cm with a 60° angle, and Triangle B has sides of 9 cm and 12 cm with a 60° angle, they can be shown to be similar. Thus, the SAS similarity theorem is validated in this case.


Explanation:

Proving Triangle Similarity Using the SAS Similarity Theorem

To prove that two triangles are similar using the SAS similarity theorem, you need to establish two critical conditions:

  1. Two sides of one triangle are in proportion to two sides of the other triangle.
  2. The included angle between those two sides is equal in both triangles.

For example, consider two triangles, Triangle A and Triangle B:

  • In Triangle A, the lengths of sides are 6 cm and 8 cm, and the included angle is 60°.
  • In Triangle B, the lengths of the corresponding sides are 9 cm and 12 cm, and the included angle is also 60°.

To apply the SAS similarity theorem, we check:

  • For Triangle A: Side 1 = 6 cm, Side 2 = 8 cm.
  • For Triangle B: Side 1 = 9 cm, Side 2 = 12 cm.

The ratio of the sides is:

  • 6/9 = 2/3
  • 8/12 = 2/3

Since both ratios are equal (2/3), and the included angles are equal (60°), we can conclude that Triangle A is similar to Triangle B by the SAS similarity theorem.


Learn more about Triangle Similarity here:

https://brainly.com/question/29249755


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