1. **Stating the problem:** We are given two triangles, one acute with one angle marked and one side marked with a single tick, and the other a right triangle with the vertical leg marked with two ticks and a right angle indicated. We need to determine the relationship between these triangles and whether they can be proven congruent. 2. **Analyzing the given information:** - The left triangle is acute with one angle marked (let's call it $\angle A$) and one side marked with a single tick (let's call this side $a$). - The right triangle is a right triangle with a right angle (let's call it $\angle C = 90^\circ$) and the vertical leg marked with two ticks (let's call this side $b$). 3. **Important rules for triangle congruence:** - Triangles are congruent if they satisfy any of the following criteria: SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or HL (hypotenuse-leg for right triangles). 4. **Checking for congruence:** - Since one triangle is acute and the other is right-angled, they cannot be congruent because their angle measures differ fundamentally. - The right triangle has a $90^\circ$ angle, while the acute triangle has all angles less than $90^\circ$. 5. **Determining the relationship:** - The triangles may be similar if their corresponding angles are equal. - However, since one has a right angle and the other does not, they cannot be similar either. 6. **Conclusion:** - The two triangles are related by having some marked sides and angles but are neither congruent nor similar due to the difference in angle measures. **Final answer:** The two triangles are not congruent because one is right-angled and the other is acute, so the triangles cannot be proven congruent.