1. **Problem statement:** We have a right triangle with a 90° angle at vertex A and a 45° angle between side AC and a dashed line inside the triangle. We want to analyze the triangle's properties. 2. **Key fact:** In a right triangle, the sum of the other two angles is 90°. Since one angle is 45°, the remaining angle must also be 45°. 3. **Conclusion:** This is a 45°-45°-90° triangle, which is an isosceles right triangle. 4. **Properties of a 45°-45°-90° triangle:** - The legs are congruent. - The hypotenuse is $\sqrt{2}$ times the length of each leg. 5. **Formula:** If each leg has length $x$, then the hypotenuse $h$ is given by $$h = x\sqrt{2}$$ 6. **Explanation:** Because the two legs are equal, the triangle is symmetric, and the angles opposite those legs are equal (both 45°). 7. **Summary:** The triangle with angles 90°, 45°, and 45° has legs of equal length and a hypotenuse equal to $\sqrt{2}$ times a leg. This completes the analysis of the triangle based on the given angles.