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Discover more at www.ck12.org: http://www.ck12.org/geometry/**SSS**-**Similarity**/Here you'll learn how to determine if triangles are **similar** using Side-Side-Side.

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For **example**, for any two similar triangles ΔABC and ΔDEF, Area of ΔABC/Area of ΔDEF = (AB) 2 /(DE) ... Is **SSS** a **similarity** **theorem**? **SSS** **Similarity** **Theorem**. By definition, two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. It is not necessary to check all angles and sides.

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**Example** 2: Given the following triangles, find the length of s. Solution: Step 1: The triangles are similar because of the RAR rule. Step 2: The ratios of the lengths are equal. Answer: The length of s is 3. **SSS** Rule. The Side-Side-Side (**SSS**) rule states that If two triangles have their corresponding sides in the same ratio, then they are similar. By the **SSS** Congruence **Theorem** , it follows that ¤PSQ £ ¤LMN.Finally, use the definition of congruent triangles and the AA **Similarity** Postulate to conclude that ¤RST~ ¤LMN. **EXAMPLE** 1 GOAL 1 Use <b>**similarity**</b> <b>**theorems**</b> <b>to</b> prove that two triangles are **similar**.

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This page titled 2.6: **The SSS Theorem** is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Henry Africk (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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Objectives Prove certain triangles are **similar** by using AA, **SSS**, and SAS. Use triangle **similarity** to solve problems. There are several ways to prove certain triangles are **similar**. The following postulate, as well as the **SSS** and SAS **Similarity Theorems**, will be used in proofs. Since , B E by the Alternate Interior Angles **Theorem**.

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Use the **SSS** **Similarity** **Theorem** to determine if triangles are similar. Click Create Assignment to assign this modality to your LMS. We have a new and improved read on this topic. Click here to view We have moved all content for this concept to for better organization. Please update your bookmarks accordingly.

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**sss similarity theorem**examples. by | Apr 20, 2022 | school compound wall design ...**EXAMPLE**2 Use the**SSS Similarity Theorem**4 18 = 12(x – 1) 72 = 12 x – 12 7=x Cross Products Property Simplify. Solve for x. STEP 2 Check that the side lengths are proportional when x = 7.- 7-3 Triangle
**Similarity**: AA,**SSS**, SAS There are several ways to prove certain triangles are**similar**. The following postulate, as well as the**SSS**and SAS**Similarity Theorems**, will be used in proofs just as**SSS**, SAS, ASA, HL, and AAS were used to prove triangles congruent.. "/> **Theorem**8-1 Side-Angle-Side**Similarity**(SAS~) In this image Angle A is congruent to Angle P and both sides ( Side AC and Side AB/Side PR and Side PQ) are proportional to the other two sides of the other triangles because 4/8 equals 1/2 when you simplify it and 3/6 equals 1/2 when you simplify it making both sides proportional to each other.- Discover more at www.ck12.org: http://www.ck12.org/geometry/SAS-
**Similarity**/Here you'll learn how to determine if triangles are similar using Side-Angle-Side...