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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:

The SAS similarity theorem requires that two triangles have one pair of corresponding sides in proportion and the included angles equal. For example, if Triangle ABC with sides AB = 4 cm and AC = 3 cm has an angle ∠A = 60°, and Triangle DEF with sides DE = 8 cm and DF = 6 cm also has an angle ∠D = 60°, then they are similar. Thus, both triangles demonstrate this theorem effectively.


Explanation:

SAS Similarity Theorem


The SAS similarity theorem states that if two triangles have one pair of corresponding sides that are in proportion and the angles included between those sides are equal, then the triangles are similar.


Necessary Information


To prove two triangles are similar by the SAS similarity theorem, you need:



  2. The lengths of two sides from each triangle must be in proportion.

  4. The angle formed between those two sides must be the same in both triangles.


Example of Similar Triangles


Consider two triangles, Triangle ABC and Triangle DEF:



  • In Triangle ABC, the lengths of side AB = 4 cm, AC = 3 cm, and the included angle ∠A = 60°.

  • In Triangle DEF, the lengths of side DE = 8 cm, DF = 6 cm, and the included angle ∠D = 60°.


To show that Triangle ABC is similar to Triangle DEF using the SAS similarity theorem, we verify:



  • Proportions: AB/DE = 4/8 = 1/2 and AC/DF = 3/6 = 1/2. Both pairs of sides are in proportion.

  • Angle: The included angle ∠A = ∠D = 60°.


Since both conditions are met, Triangle ABC is similar to Triangle DEF.


Learn more about Triangle Similarity here:

https://brainly.com/question/29249755


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