Liu Yichen put his schoolbag on his desk and went to take a shower.

Passing by Deng Lingze's desk, I saw Deng Lingze holding a pen and looking at a question with a sullen face. This was the second question of a mathematics paper. It drew a four-sided pyramid. It was obviously a test of geometry knowledge.

"Liu Yichen, I can't solve a question here, can you help me?" Deng Lingze suddenly said, then he was startled and shook his head funny: "I'm really stupid, you are just in the first grade of high school, this question

The question is the real question of this year’s college entrance examination, how can you do it!”

Liu Yichen glanced at the topic: "As shown in the figure, in the square pyramid p-abcd, the surface pad⊥, the bottom surface abcd, the side edges pa=pd=2^0.5, the bottom surface abcd is a right-angled trapezoid, where bc∥ad, ab⊥ad,

ad=2ab=2bc=2, o is the midpoint of ad. (1) Verify: po⊥ plane abcd; (2) Find the size of the angle between straight lines pb and cd on different planes; (3) Whether there is a point q on the line segment ad

, so that its distance from plane pcd is 3^0.5/2? Assuming it exists, find the value of aq/qd; assuming it does not exist, please explain the reason."

Liu Yichen pondered for a moment, then said with a smile: "This question is not difficult!"

Under Deng Lingze's surprised eyes, Liu Yichen drew this quadrilateral on the draft paper, and then wrote (1) to prove: In △pad, pa=pd, o is the midpoint of ad, so po⊥ad, and

The side pad ⊥ bottom surface abcd, so the po ⊥ plane abcd.

(2) Connect bo. In the right-angled trapezoid abcd, bc∥ad, ad=2ab=2bc, there is od∥bc, and od=bc, so the quadrilateral obcd is a parallelogram, so ob∥dc, it can be known from (1),

po⊥ob, ∠pbo are acute angles, so ∠pbo is the angle formed by the straight lines pb and cd in different planes...

While Deng Lingze was stunned, Liu Yichen took less than three minutes to complete the answers to the three short questions of this question, and it seemed that there was nothing wrong with him.

Liu Yichen took a change of clothes, soap, shower gel and shampoo and headed to the bathroom, leaving only a stunned Deng Lingze.

After a while, Deng Lingze took the scratch paper left by Liu Yichen, pushed up his glasses, stared at the topic, frowned slightly, and fell into deep thought.

Now in the third year of senior high school in Qingcheng No. 1 Middle School, the teaching work of the entire high school knowledge points has been completed as early as the last stage of the second semester of the second semester of high school. Except for a few subjects, all other subjects have begun to enter the first round of review. Before the college entrance examination comes, the entire senior year of high school

It is necessary to complete three rounds of review, continue to further compress and refine according to the college entrance examination syllabus, and strengthen students' training on test points and questions.

So for this question, when Liu Yichen actually wrote down the answer, Deng Lingze quickly understood the idea of ​​answering the question and the corresponding knowledge points.

But what he couldn't figure out was how could Liu Yichen, a freshman in high school, have such deep knowledge?

And in such a short time...

Deng Lingze bit his lip.

Suddenly, Deng Lingze felt that he had some doubts about life. He had been studying hard in high school for two years, and the countdown to the college entrance examination was officially approaching. As a result, he found that he seemed to be worse than a rookie entering high school. This...

How to prepare for the college entrance examination?

If you are forced to be a top student, you are still a top student. Can a top student be looked down upon by a bad student?

Are all mortals scum in front of top academics?

Alas, it’s too difficult to explain the world of academic masters to ordinary people. Forget it, I won’t explain it anymore. I’ll just swim in the sea of ​​questions. Only the sea of ​​learning is where I belong and can bring me happiness.
Chapter completed!