Many students can only "talk about the topic" when doing a topic, but it is not good to appear in another form, so repeated practice is very helpful to improve their grades. Give a simple example:

In the figure 1, AD is the height on the hypotenuse BC of the right angle △ABC. Verify AC? =CD*CB .

The proof is simple, ∫≈ 1 =∠B (why? ),

△ ADC △ ABC, △ CD: AC = AC: CB, which is AC? =CD*CB .

Because some students didn't fully understand the essence of this problem, he changed it to Figure 2, and he won't do it again!

It is known in figure 2 that ∠ 1=∠B, verify AC? =CD*CB .

In fact, these two problems have only changed from special graphics to general graphics, and their essence has not changed at all, which proves that:

∠∠ 1 =∠b, ∠C, ∴△ACD∽△ABC, ∴ CD: AC = AC: CB, that is, AC? =CD*CB .

Topics like this are more useful after learning the knowledge of circles: they are used in both the power theorem and the tangent theorem of circles.

There are also some topics that can be exchanged with one of the conditions in the topic design through the conclusion, and then proved, so that the essence of the topic can be clarified, and you will solve it no matter what form it appears in the future. This is also called: draw inferences from others, draw inferences from others.