Cho tứ giác ABCD. AC giao BD tại P. (AP B) cắt (CP D) tại Q. Gọi H1, H2, H3, H4 lần lượt là trực tâm của các tam giác ABP, AQB, CQD, CPD. Chứng minh rằng tứ giác H1H2H4H3 là hình bình hành.

Bạn học đến chương 3 hình học lớp 9 chưa

a)\(\sqrt{\left(3-2\sqrt{2}\right)^2}\) + \(\sqrt{\left(3+2\sqrt{2}\right)^2}\) = \(\left(3-2\sqrt{2}\right)+\left(3+2\sqrt{2}\right)\) =\(3-2\sqrt{2}+3+2\sqrt{2}\) =\(6\)

b)\(\sqrt{\left(5-2\sqrt{6}\right)^2}-\sqrt{\left(5+2\sqrt{6}\right)^2}=\left(5-2\sqrt{6}\right)-\left(5+2\sqrt{6}\right)=5-2\sqrt{6}-5-2\sqrt{6}\)\(=-4\sqrt{6}\)

c)\(\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}=\sqrt{5}-\sqrt{2}+\sqrt{5}+\sqrt{2}=2\sqrt{5}\)

d)\(\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}=\sqrt{2}+1-5+\sqrt{2}=2\sqrt{2}-4\)

e)\(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}=2-\sqrt{3}+\sqrt{3}-1=1\)

f)\(\sqrt{\left(3+\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}=3+\sqrt{2}-\sqrt{2}+1=4\)

48. My brother whose house was broken in called the police.

49. Mary was too very tired to study more.

50.If Emily wasn't sick today, she could go to school.

51.Although my grandparents are very busy, they spend a lot of time taking care of us.

52. The floor hasn't been cleaned yet.

53.We haven't seen our grandfather for five month.

54. I wish I could remember the answers to these questions.

55. I spent three hours cleaning the house yesterday.