There are generally two ways to solve conclusive exploratory problems with geometric figures:
(1) Use geometric tools (ruler, protractor) to measure the conclusion of judging questions and turn exploratory questions into traditional ones. For example, item (1) of the last question in 2002: pq=pb is obtained after measuring with a ruler, and then pq=pb is proved by the method of triangle congruence.
(2) Affirm or deny some conclusions through calculation. Item (3) of the last question in 2002 was determined by calculation, so that △pcq became the position of point Q of isosceles triangle. If there is no solution in the calculation process, it means that △pcq cannot be an isosceles triangle.
If you encounter a conclusive exploratory problem in algebra, you will generally confirm or deny the conclusion through calculation.
The last question in 2000 (1): When point P moves on arc ab, are there any line segments with the same length among line segments go, gp and gh? If yes, please point out the line segment and find out its length. Can you answer this question? Measure with a ruler? Method can also be passed? Calculation? The method. When measuring with geometric tools under dynamic conditions, it is necessary to make the measurement results of two moving points in different positions the same, so as to draw a conclusion.
In recent years, the idea of separate discussion often appears in the senior high school entrance examination questions. For example, item (3) of the last question in 2000: If △pgh is an isosceles triangle, try to find the length of line segment pH. According to the idea of classified discussion, it should be discussed in three situations. However, because the topic requires the length of ph, the case of gh=gp need not be discussed. Another example is item (2) of the last second question in 2002. When △brt is similar to △aoc, find the coordinates of point R. Because these two triangles are right triangles, we should discuss them in two cases. Another example is the last question in 2002, which has been introduced above. This is an exploratory question. In addition, it is also a classified discussion topic. Question (3): Is it possible for △pcq to become an isosceles triangle when point P slides on line ac? If the midpoint of ac is O, then the isosceles triangle obtained by sliding point P on ao and point P on oc is different and should be discussed in different categories. The last second question in 2003: It is known that the image of quadratic function passes through point A and point B and intersects with Y axis at point C, but the opening direction of the problem is not clear, so it should be discussed in different categories when solving the problem. The last second question in 2004: The topic requires finding the area of △aoc when the circle O is tangent to the circle A, because it does not say whether the two circles are inscribed or circumscribed, so it should be discussed in categories.
The topic that helps us to explore the conclusion with geometric tools is also called measurement inquiry. The last question in 2000 introduced above belongs to measurement inquiry. In addition, the last second question of 200 1 and the last question of 2003 are all inquiry questions of measurement type.
The last question in 2004: Because the conclusion of item (2) is unclear and the conclusion of item (3) is unknown, after verifying the conclusion of item (1), we should imitate the answering process of item (1) to complete the answers of items (2) and (3), so it is also called imitation inquiry question.
The exploratory questions of testing in recent ten years include: conclusive exploratory questions, imitative exploratory questions, measurement exploratory questions and classified exploratory questions.
When reviewing the comprehensive questions, don't forget to review the basic content. A good review of the basic content will lay a solid foundation for answering comprehensive questions. Tall buildings have risen from the ground? That's the truth. After reviewing the basic content, you will have the ability to answer comprehensive questions. The closer we get to the senior high school entrance examination, the more we should combine reviewing basic content with answering comprehensive questions.