Before learning this lesson, we have clearly learned the nature and determination of parallelogram, which is a foundation for this lesson. Learn the nature of the median line, practice the process of using existing knowledge proof, and experience the basic steps of general proof. Key points: difficulties in the nature of the median line: the process of proving the nature of the median line.
Operation method
Students, we have learned about triangles before. Can we make a triangle into a parallelogram with the same area by cutting, pasting and splicing it? See the PPT [blackboard writing topic].
We can see that it takes AB and AC as the midpoint, and then what happens? Who can tell us? Oh, you can see that △ CFE is obtained by rotating △ ADE 180 ° around point E, so we can get a parallelogram BCFD. From the above practice, we can guess what is the relationship between the midpoint line on both sides of the triangle and the third side? Can you prove your conjecture?
In mathematics, we call the line connecting the midpoints on both sides of a triangle the median line of a triangle. In this lesson, we will conjecture and prove the nature of the median line of a triangle. Can anyone give us some ideas? OK, this student. You say, well, please sit down. Students, what he said is that we can prove that △ ADE and △ CFE are congruent, and then we can get that DFCB is a parallelogram, and then we can get the relationship.
So, who will tell me the detailed steps? No response. It seems that the students have questions about this step. Let's discuss it in groups. OK, I think the students are very active in the discussion. The group leader, you say, oh, you said to extend DE to F so that EF=DE and then connect CF, we have the condition ① DE=EF ② ∠ 1=∠ 2 ③ AE=CE, so △ AED ∨ △ CEF (SAS) ∠ A=∠ ACF so, AB ‖ CF, so BCFD is a parallelogram so DE ‖=? DF∥＝？BC。
Students, is he right? I have got the answer from the students' expressions. Then, we have proved a proposition: the median line of a triangle is parallel and equal to the bottom half. Have you mastered it? You said that you have mastered it. Oh, let me test you. Look at the examples after the textbook. If we change the triangle into a trapezoid, is there any similar conclusion? Think about it after class.
In this lesson, we learned the nature of the median line of a triangle and gave its proof. Then we should also link theory with real life and try to use the knowledge we learned in life, OK? OK, class is over.
