1. **State the problem:** We need to prove that triangle $\triangle EFX$ is congruent to triangle $\triangle GHX$ based on the given markings. 2. **Identify given information:** - Side $EF$ is congruent to side $GH$ (both have three matching marks). - Side $FX$ is congruent to side $GX$ (both have two matching marks). - Side $EX$ is congruent to side $HX$ (both have one matching mark). - Angles at $E$ and $H$ are congruent. - Angles at $F$ and $G$ are congruent. 3. **Recall congruence criteria:** Triangles are congruent if they satisfy any of the following: - SSS (Side-Side-Side): all three sides equal. - SAS (Side-Angle-Side): two sides and the included angle equal. - ASA (Angle-Side-Angle): two angles and the included side equal. - AAS (Angle-Angle-Side): two angles and a non-included side equal. - RHS (Right angle-Hypotenuse-Side) for right triangles. 4. **Apply the SSS criterion:** Since all three pairs of corresponding sides are marked equal: $$EF = GH, \quad FX = GX, \quad EX = HX$$ This satisfies the SSS criterion. 5. **Conclusion:** By the SSS congruence rule, $\triangle EFX \cong \triangle GHX$. This reasoning shows the two triangles are congruent because all their corresponding sides are equal in length.