Fractions and Attached Text: Slope and Pythagorean Theorem in a Right Triangle

① This GeoGebra example constructs a right triangle and displays the lengths of its two legs (rise and run) as fractions, with attached text showing the slope, squared side lengths, and other mathematical relationships, vividly demonstrating the combination of fractions and geometry. ② Core mathematical concepts include fraction representation, slope (rise/run), the Pythagorean theorem (a²+b²=c²), the orthocenter, and introductory applications of quadratic functions and parametric curves. ③ Construction highlights: commands such as Line, OrthogonalLine, Intersect, Polygon, and SurdText are used to build the right triangle and its perpendicular lines; objects include B, A, run, rise, text1, text2, slope, text3, g, h, i, C, poly2, b_2, a_2, c_2, B1, A1, text4, and text5, where the text objects attach fraction and formula labels. ④ Suitable for middle school to high school students learning fraction operations, slope concepts, verifying the Pythagorean theorem, and exploring dynamic geometry with GeoGebra, as well as for teachers creating interactive math lessons.