Further exploration of the nature of the parallelogram and its application

Parallelogram in the study of parallel lines and triangles, the triangle is parallel to the line and application of knowledge and deepening, while the back is to learn a rectangle, diamond, square, round, even laying the foundation of high-dimensional geometry, plays a linking bridge role.

The nature of the parallelogram
Parallelogram with more nature, such as a parallelogram equal to the angle and the side with nature, etc. In addition, the use of parallel lines can know the nature of interior angles of a parallelogram are equal, while extension cords can also refer to the nature of parallel lines drawn corresponding angles are equal, these properties are in the actual problem solving is often used, and these properties can be shared between "transformation." First of all, makes up the use of two parallel sides congruent triangles, and then, from that fight on congruent triangles out of the parallelogram, the parallelogram can be drawn "from the opposite side," "diagonal equal" in nature, in particular, that better reflect the nature of the mathematical ideas through the rotation and translation triangle, prove that conclusion, as teachers in the instructional design process needs to focus on transformation of thinking through, the parallelogram is transformed into a triangle to solve problems, we can better address the focus of teaching content.

Add guides into a triangle to a parallelogram
Add guides into the parallelogram quadrilateral triangle is a junior research problems common method, it is also an important manifestation of ideas into Connect diagonal, the parallelogram into two congruent triangles and congruent triangles using nature of the parallelogram drawn nature of the study is an important method of parallelogram, and students of rotation, the center symmetry little knowledge about the use of graphics to explore the transformation of the parallelogram may have some difficulties, the past, students have to use axes isosceles symmetry to explore the nature of the experience and understanding, as long as the appropriate lead teachers, students also will be ripe for self-exploration. In addition, for middle school students, through the measure, summarized the nature of a parallelogram is not difficult.

Therefore, in the actual teaching should allow students through the operation, to explore the changing nature of a parallelogram on the basis of the nature and can be found further proof, which requires them to come to the preliminary nature of the use of logical reasoning, rather than through intuitive operation induction has been the nature of the parallelogram, then let the students to use nature to solve some simple problems.

Many students often do not know how the guides do, why, there are several different approaches and other issues. In fact, if the students explore their own problems, we should focus on training and exercise their means and methods to explore the issue, and understand "the fold" can draw the center line, angle bisector, median lines, "translation" can draw parallel lines, to find corresponding angles, interior angles, same side interior angles, etc., "spin" can draw 60 °, 90 °, 180 ° of the angle of the triangle so constructed as to guide the students to add the appropriate auxiliary line, the unknown into the known, the use of already learned knowledge to solve new problems, improve their analytical, problem-solving abilities. Of course, the students in the school over the nature of the parallelogram, the parallelogram can use nature to solve problems, not through adding auxiliary lines into parallel lines or triangles to solve, in the construction of congruent triangles in circles, but the use of new knowledge to solve the problem, which would be the nature of students proficient in the habit of this.

Third, the parallelogram nature of proofs in the application
Parallelogram in the middle of the many properties of geometric proofs of the problem-solving process is often used, for example, that the same line, that corners are equal, that sub-segment and bad times, so that problem-solving in two vertical lines are common, so parallel quadrilateral geometric problem-solving in the junior plays a very important role on the nature of the flexible application of the parallelogram is the focus of teaching junior high school geometry and difficult, for example, showed that the two segments are equal problems, known: M is open isosceles triangle ABC The bottom edge of the point, over M for ME / / AC cross AB at E, for the MF / / AB cross-AC in F, Explain: BE = AF, CF = AE. we must first discuss this topic AEMF quadrilateral is a parallelogram , re-use of a parallelogram the opposite side of nature, combined with the nature of the isosceles triangle be resolved. Links to free download http://www.hi138.com