Advances in International Applied Mathematics

We call two figures whose corresponding angles are equal and whose corresponding sides are proportional similar. The similarity of figures is an extremely important element of plane geometry in middle school math, and it is a key examination in the middle school math test. The knowledge of similar triangles has two aspects, one is derived from similar triangles themselves, and the other is closely related to congruent figures and similar figures. It usually appears in the middle school examination paper as a finale question, which puts high demands on students problem solving ability, and at the same time, it will involve a variety of mathematical ideas and methods, such as combination of numbers and shapes, classification, equations, functions and so on. In this paper, a 2023 Shanghai Jiading District Secondary School Examination second-mode fill-in-the-blank finale questions, using the form of one problem with multiple solutions to explore similar triangles solution strategy, in order to students to master the basic knowledge of junior high school mathematics, basic skills, to improve the analysis of the problem, problem solving ability, and then enhance the students geometric intuition, the concept of modeling, logical reasoning and other mathematical core literacy.

Similar triangles; Four points coexist with a circle; Middle School Mathematics