Cho tứ diện ABCD có \(DA \bot \left( {ABC} \right)\), ABC là tam giác cân tại A. Gọi M là trung điểm của BC. Gọi G, K lần lượt là trọng tâm của tam giác ABC và DBC. Góc giữa hai đường thẳng GK và AB bằng?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Vì K là trọng tâm của tam giác DBC, DM là đường trung tuyến của tam giác DBC nên \(\frac{{MK}}{{MD}} = \frac{1}{3}\)
Vì G là trọng tâm của tam giác ABC, AM là đường trung tuyến của tam giác ABC nên \(\frac{{MG}}{{MA}} = \frac{1}{3}\)
Tam giác DMA có: \(\frac{{MK}}{{MD}} = \frac{{MG}}{{MA}}\left( { = \frac{1}{3}} \right)\) nên GK//AD
Mà \(AD \bot \left( {ABC} \right)\) suy ra \(GK \bot \left( {ABC} \right)\). Mà \(AB \subset \left( {ABC} \right) \Rightarrow GK \bot AB\)
Do đó, góc giữa hai đường thẳng GK và AB bằng \({90^0}\).
Đáp án C.
Bộ Đề Kiểm Tra Giữa Học Kì II - Toán 11 - (Năm học 2023 - 2024) - Các Trường THPT Trên Toàn Quốc là tài liệu học tập giúp học sinh ôn tập và củng cố kiến thức đã học thông qua các câu hỏi trắc nghiệm đa dạng. Tài liệu không chỉ giúp học sinh rèn luyện kỹ năng tư duy, phân tích mà còn hỗ trợ việc ghi nhớ thông tin quan trọng một cách hiệu quả.
Câu hỏi liên quan
Các dạng địa hình nào chiếm phần lớn diện tích khu vực Mỹ Latinh?
Hội nghị thượng đỉnh về trái đất được tổ chức năm 1992 ở thành phố nào sau đây?
Quyền khiếu nại của công dân không bao gồm nội dung nào sau đây?
Read the following passage about the Second Acts That Inspire and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Life often presents us with unexpected challenges that force us back to the drawing board. Whether due to personal setbacks, career changes, or unforeseen circumstances, the courage to begin again can lead to remarkable transformations. Many inspiring individuals have shown that it's never too late to reinvent oneself and pursue new dreams. Throughout history, countless people have overcome seemingly impossible situations through sheer determination.
[I] Take J.K. Rowling, for instance. Before becoming a literary sensation, she was a struggling single mother living on welfare. [II] Her determination eventually paid off when her books became a global phenomenon, proving that setbacks can become stepping stones to success. [III] This remarkable turnaround demonstrates how resilience and unwavering belief in oneself can overcome seemingly insurmountable obstacles. Despite facing depression and financial hardship, she never gave up on her dreams. [IV]
Colonel Harland Sanders' story is another testament to the power of starting anew. At the age of 65, when most people contemplate retirement, he found himself struggling financially after his restaurant failed. Instead of giving up, he traveled across America, sleeping in his car while pitching his chicken recipe to restaurant owners. His recipe for success wasn't just about the perfect blend of herbs and spices; it was about persistence and determination. After facing over 1,000 rejections, he finally established Kentucky Fried Chicken, which grew into a global empire. His unwavering spirit and dedication inspired generations of entrepreneurs worldwide.
These inspiring stories remind us that failure is not final, but rather a chance to redirect our path. Every setback carries the seed of an equal or greater opportunity, and sometimes the end of one chapter is simply the beginning of a better one. The key lies in having the courage to take that first step, even when the future seems uncertain. As these remarkable individuals have shown, it's never too late to rewrite your story and create a powerful second act. Their journeys teach us that persistence and courage ultimately lead to success.
Where in paragraph 2 does the following sentence best fit?
Against all odds, she persevered through numerous rejections and continued writing her Harry Potter manuscript in local cafes.
Thực dân Pháp hoàn thành cơ bản cuộc xâm lược Việt Nam khi nào?
Nội dung nào sau đây là nhiệm vụ của Sử học?
Nước ta rơi vào ách đô hộ của nhà Minh đánh dấu bằng sự kiện nào?
Tập nghiệm của bất phương trình \({{x}^{2}}-3x+2<0\) là
Phát biểu nào sau đây không đúng?
Các nhân tố môi trường có ảnh hưởng rõ nhất vào giai đoạn nào trong quá trình phát sinh cá thể người?
Vào năm 2004 sản phẩm trí tuệ nhân tạo nào đã đến Việt Nam?
Read the following passage about Wildlife Conservation in Africa and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Wildlife conservation in Africa is vital for preserving biodiversity and ensuring the survival of iconic species such as elephants, lions, and rhinos. [I] The continent is home to some of the world’s most diverse ecosystems, including savannahs, rainforests, and deserts. [II] Conservation efforts involve strategies like protecting habitats, combating poaching, and raising awareness about the importance of wildlife. [III] Despite challenges, success stories demonstrate the positive impact of these efforts. [IV]
One notable example comes from Kenya, where anti-poaching initiatives and community engagement have helped stabilize elephant populations in Amboseli National Park. Similarly, in South Africa, rhino conservation programs use advanced technologies like drones and GPS tracking to monitor and protect vulnerable animals. These efforts not only safeguard wildlife but also promote eco-tourism, which supports local economies.
However, wildlife conservation in Africa faces persistent threats. Habitat loss due to agricultural expansion and urbanization continues to endanger species. Climate change exacerbates these challenges, altering migration patterns and threatening ecosystems. Furthermore, poaching and the illegal wildlife trade remain significant concerns, driven by global demand for products such as ivory and rhino horn.
To overcome these challenges, conservationists emphasize the need for international collaboration and local community involvement. Initiatives like eco-tourism provide financial incentives for communities to protect wildlife. Governments, NGOs, and individuals must work together to ensure the survival of Africa’s unique species for future generations.
Which of the following can be inferred from the passage?
When he was a student, his father gave him a monthly ______ towards his expenses.
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions from 41 to 45.
When parents name their children, they often take into consideration their own preferences, family traditions, or beliefs. In many European cultures, parents typically select names based on family connections, often honoring grandparents or ancestors. For instance, in Italy, children are commonly named after their grandparents, starting with the father's parents and then the mother's. Similarly, in Eastern Europe, children may be named after their deceased relatives to protect them from harm.
In some Asian countries, the naming process may involve the child's grandfather or a fortune-teller, who chooses a name believed to shape the child's character. Names might be inspired by elements like fire, water, earth, wood, or metal, or they may convey qualities such as beauty, strength, or kindness.
African cultures also have unique naming traditions, such as in Ghana's Akan culture, where a child's name is determined by the day of their birth. Each day has specific names for boys and girls, reflecting characteristics associated with that day. For example, a boy born on Friday might be named Kofi, symbolizing a "wanderer" or "explorer" while a girl born on the same day could be named Afua, also representing a traveler.
No matter where a name originates, it holds significant meaning and reflects the child's cultural heritage. Whether chosen out of preference or dictated by tradition, a child's name is a cherished and respected gift.
The word "dictated" in the passage is closest in meaning to________.
Bộ máy nhà nước Cộng hoà xã hội chủ nghĩa Việt Nam gồm có mấy đặc điểm cơ bản?
Đặc trưng cơ bản nhất của cơ chế thị trường là gì?
Read the following passage about Key to Addressing Poverty, Gender Disparities, and Environmental Challenges and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 18 to 22.
Social issues are problems that affect a large number of people in society, often creating inequality and hardship. One of the most significant social issues today is poverty. (18)_________, such as food, shelter, and education. In many parts of the world, (19)_________, with families trapped in a cycle of deprivation. While poverty is a complex issue, it is often connected to factors like unemployment and lack of access to education. These factors make it hard for individuals to escape the cycle and improve their lives. To address poverty, governments and organizations must create sustainable policies that focus on education, healthcare, and employment opportunities.
Another pressing issue is gender inequality. In many countries, women still face discrimination in areas like employment and education, limiting their opportunities for personal and economic growth. Even in developed nations, women earn less than men for doing the same work. (20)_________, as people demand equal rights and opportunities for all genders. Moreover, gender inequality can also affect women's health and safety, (21)_________.
Finally, environmental degradation, like pollution and climate change, is a growing global concern. Environmental damage, (22)_________, especially in poorer regions, often affects them the most. The increasing frequency of natural disasters, caused by climate change, is also putting immense pressure on vulnerable populations. Tackling these issues requires a collective effort from both individuals and governments. Only through cooperation and sustainable practices can we hope to create a more equitable and livable world for future generations.
Phát biểu nào là đúng khi nói về Hằng?
Ở hệ thống nhiên liệu của động cơ Diesel tích áp
Lực nào đóng vai trò là lực đẩy nước từ rễ lên thân, lên lá?