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If △abc ≅ △xyz, which sides and angles are congruent to each other?

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Final answer:

In congruent triangles ABC and XYZ, side AB is congruent to side XY, BC to YZ, CA to XZ, and corresponding angles A, B, C are congruent to angles X, Y, Z, respectively.

Step-by-step explanation:

If △abc ≅ △xyz, this means that triangle ABC is congruent to triangle XYZ. Congruency in triangles implies that all corresponding sides and angles are equal in measure. Therefore, side AB is congruent to side XY, side BC to YZ, and side CA to XZ. Similarly, angle A is congruent to angle X, angle B to angle Y, and angle C to angle Z. This follows from the basic Triangle Congruence postulates such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

To demonstrate Triangle Congruency, it's important to ensure that all corresponding sides and angles match. For a better understanding, consider two triangles laid over each other such that every vertex of one triangle touches the vertex of the other. If they perfectly overlay, they are congruent. Geometric figures like triangles play a crucial role in various geometric constructions and can be found in several real-life applications from engineering to art.

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