Indicate which triangles are congruent. Be sure to have the...

Indicate which triangles are congruent. Be sure to have the correspondence of letters correct. (FIGURE CANNOT COPY)
$$\begin{aligned}&\triangle \mathrm{BOW} \cong ?\\&\text { Why is } \angle 1 \cong \angle 2 ?
\end{aligned}$$

Key Concepts

Triangle Congruence

Triangle congruence is a fundamental concept in geometry where two triangles are considered congruent if all their corresponding sides and angles are equal. Establishing triangle congruence ensures that one triangle can be mapped exactly onto the other through rigid motions such as rotation, reflection, or translation.

Congruence Postulates

Congruence postulates such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS) provide the criteria for proving that two triangles are congruent. These postulates allow one to determine congruence by verifying that a specific set of corresponding parts (sides and/or angles) are equal in the two triangles.

Correspondence of Vertices and Angles

When stating that two triangles are congruent, it is crucial to maintain the proper correspondence of vertices and angles. This means that the order in which the triangle’s points are listed reflects which angles and sides are being compared. Proper correspondence ensures clarity in identifying which parts of the triangles are congruent.

Angle Congruence

Angle congruence in geometry refers to the concept that two angles are congruent if they have the same measure, regardless of their orientation or location in a figure. In triangle congruence problems, demonstrating that one pair of corresponding angles (such as angle 1 and angle 2) are congruent is often a key step in applying congruence postulates and CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

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