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You can build two triangles that have the same side lengths but are not congruent. A. True

Ask by Higgins Carter. in the United States
Jan 23,2025

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The statement is **False**. In Euclidean geometry, two triangles with the same side lengths must be congruent.

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The Deep Dive

Absolutely true! This phenomenon occurs in the case of ambiguous triangles, which are often identified using the Side-Side-Angle (SSA) condition. Here’s the twist: given two sides and an angle that isn’t between them, you can actually create two different triangles. It’s like having the same set of Lego pieces but building two distinct models based on how you place the pieces! Thinking in practical terms, this concept plays a significant role in fields like architecture and design. When working on a project with specific dimensions, understanding that certain combinations can lead to multiple configurations can help architects and designers create various layouts while adhering to the same measurement standards. It’s like finding multiple paths to reach a destination!

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