The text describes a geometry problem involving triangle ABC, where specific conditions and properties of right triangles are being used.

1. In the first problem, triangle ABC is defined as a right triangle with angle A equal to 90 degrees. It mentions a perpendicular line from point B to line AC at point D, as well as constructing point E on line AC. The goal is to prove that two angles are equal: \( \angle EDC = \angle DEC \).

2. The second problem states that triangle ABC is a right triangle at A. A line AH is drawn perpendicular to BC from point A. From point C, a line is drawn parallel to AH that intersects AB at point I. The tasks involve proving two statements about angles:
a) \( \angle AHC = \angle BAH \)
b) \( \angle B = \angle ICA \)

These types of problems generally focus on angle relationships in triangles, especially those involving right angles and parallel lines. If you need more detailed explanations or solutions for these problems, feel free to ask!