sum of interior angles of polygons

Sec 2 _Investigating Figures - Sum of interior angles in polygons

MATH sum of interior angles of a polygon

Q1. A teacher designs a lesson where students compute real-life percentages such as discounts and savings. 👉 A student calculates 15% of 200 to determine savings in a purchase. What is the correct result? A. 20 B. 25 C. 30 D. 35 Q2. In a classroom activity, learners compare numbers to find the highest common factor for grouping materials evenly. 👉 What is the GCF of 24 and 36? A. 6 B. 8 C. 12 D. 18 📘 FRACTIONS, DECIMALS, AND POWERS Q3. A learner converts fractions into percentages for data interpretation. 👉 What is 3/4 expressed as a percentage? A. 50% B. 60% C. 75% D. 80% Q4. A student models exponential growth using repeated multiplication. 👉 What is the value of 252^525? A. 25 B. 30 C. 32 D. 64 📘 ALGEBRA (EQUATIONS AND EXPRESSIONS) Q5. A teacher guides students to solve equations that represent real-life situations. 👉 Solve: 2x+8=202x + 8 = 202x+8=20 A. x = 4 B. x = 6 C. x = 8 D. x = 10 Q6. Students simplify expressions to understand relationships between quantities. 👉 Simplify: 3(x+4)−2x3(x + 4) - 2x3(x+4)−2x A. x + 12 B. x + 4 C. 5x + 4 D. 5x + 12 📘 FUNCTIONS AND GRAPHING Q7. A student analyzes a linear equation to determine its rate of change. 👉 What is the slope of y=3x−5y = 3x - 5y=3x−5? A. -5 B. -3 C. 3 D. 5 Q8. A learner evaluates functions to predict outcomes. 👉 If f(x)=2x+3f(x) = 2x + 3f(x)=2x+3, what is f(4)f(4)f(4)? A. 7 B. 9 C. 11 D. 14 📘 GEOMETRY Q9. Students explore geometric shapes and their properties through visual models. 👉 What is the sum of interior angles of a triangle? A. 90° B. 180° C. 270° D. 360° Q10. A student calculates the area of a classroom table with dimensions 8 cm by 5 cm. 👉 What is the area? A. 26 sq cm B. 30 sq cm C. 40 sq cm D. 48 sq cm 📘 MEASUREMENT AND FIGURES Q11. A learner determines the volume of a cube used in a science experiment. 👉 What is the volume of a cube with side 4 cm? A. 16 cubic cm B. 32 cubic cm C. 48 cubic cm D. 64 cubic cm Q12. Students identify shapes used in design projects. 👉 How many sides does a hexagon have? A. 5 B. 6 C. 7 D. 8 📘 STATISTICS AND PROBABILITY Q13. A teacher helps students interpret data sets using measures of central tendency. 👉 What is the mean of 4, 6, 8, 10, 12? A. 6 B. 8 C. 10 D. 12 Q14. A class experiment involves flipping a fair coin. 👉 What is the probability of getting heads? A. 1/4 B. 1/3 C. 1/2 D. 2/3 📘 WORD PROBLEMS (APPLICATION) Q15. A car travels 180 km in 3 hours during a learning task on speed. 👉 What is its average speed? A. 45 km/h B. 60 km/h C. 75 km/h D. 90 km/h Q16. Students analyze work efficiency in a project. 👉 If 5 workers complete a task in 12 days, how long will 10 workers take? A. 3 days B. 6 days C. 8 days D. 12 days Q17. A student solves a problem involving ratios in a classroom population. 👉 If the ratio of boys to girls is 3:2 and there are 30 students, how many boys are there? A. 12 B. 15 C. 18 D. 20 Q18. A learner determines the duration of a scheduled trip. 👉 A journey starts at 8:30 AM and ends at 11:15 AM. How long is the trip? A. 2 hrs 15 mins B. 2 hrs 30 mins C. 2 hrs 45 mins D. 3 hrs 15 mins Q19. A student computes simple interest for financial literacy. 👉 What is the simple interest on ₱1000 at 5% for 2 years? A. ₱50 B. ₱75 C. ₱100 D. ₱150 Q20. A learner solves a perimeter problem involving a rectangle. 👉 A rectangle has a length of 12 cm and perimeter of 34 cm. What is the width? A. 5 cm B. 7 cm C. 10 cm D. 11 cm ✅ ANSWER KEY (BASED ON YOUR REVIEWER) (All verified from your uploaded file) [ilide.info...002acd4e5a | PDF] QAnswer1C2C3C4C5B6A7C8C9B10C11D12B13B14C15B16B17C18C19C20A

The sum of the interior angles of any triangle

Using the sum of the interior angles of a triangle

Deriving the sum of interior angles in multiple ways

To the Lakota, and other indigenous people on North America's Great Plains, the bison was an essential part of their culture ( expressed in the quote on the previous page). The bison provided meat for nutrition, a hide for clothing and shelter, bones for tools, and fat for soap. The bison was also central to their religious beliefs. So, when European settlers hunted the bison nearly to extinction, Lakota culture suffered. Culture is central to a society and the identity of its people, as well as its continued existence. Therefore, geographers study culture as a way to understand similarities and differences among societies across the world, and in some cases, to help preserve these societies. Analyzing Culture All of a group's learned behaviors, actions, beliefs, and objects are a part of culture. It is a visible force seen in a group's actions, possessions, and influence on the landscape. For example, in a large city you can see people working in offices, factories, and stores, and living in high-rise apartments or suburban homes. You might observe them attending movies, concerts, or sporting events. Culture is also an invisible force guiding people through shared belief systems, customs, and traditions. Culture is learned, in that it develops through experiences, and not merely transmitted through genetics. For example, many people in the United States have developed a strong sense of competitiveness in school and business, and believe that hard work is a key to success. These types of elements, visible and invisible, are cultural traits. A series of interrelated traits make up a cultural complex, such as the process of steps and acceptable behaviors related to greeting a person in different cultures. A single cultural artifact, such as an automobile, may represent many different values, beliefs, behaviors and traditions and be representative of a cultural complex. Since culture is learned there are many ways that one generation passes its culture to the next. Children and adults learn traits three ways: • imitation, as when learning a language by repeating sounds or behaviors from a person or television • informal instruction, as when a parent reminds a child to say "please" • formal instruction, as when students learn history in school 132 HUMAN GEOGRAPHY: AP" EDITION CULTURAL COMPLEX OF THE AUTOMOBILE The automobile provides much more than just transportation, as it reflects many values that are central to American culture. Origins of Culture The area in which a unique culture or a specific trait develops is a culture hearth. Classical Greece was a culture hearth for democracy more than 2,000 years ago. New York City was a culture hearth for rap music in the 1970s. Geographers study how cultures develop in hearths and diffuse-or spread-to other places. Geographers also study taboos, behaviors heavily discouraged by a culture. For example, many cultures have taboos against eating certain foods, such as pork or insects. What is considered taboo changes over time. In the United States, marriages between Protestants and Catholics were once taboo, but they are not widely opposed now. Traditional, Folk, and Indigenous Cultures With the beginning of the Industrial Revolution in the late 18th century, modern transportation and communication connected people as never before and led to extensive cultural mixing, especially as cities have grown. The world prior to this time was very different; however, remnants of the past are still evident in our modern cultures. Traditional, folk, and indigenous cultures share some important characteristics and are often grouped together, but they do have some subtle differences. Traditional Culture Recently, the meanings of traditional, folk, and indigenous culture have begun to merge, causing geographers to debate when each should be used. Increasingly, the term traditional culture is used to encompass all three cultural designations. All three types share the function of passing down long-held beliefs, values, and practices and are generally resistant to rapid changes in their culture. Folk Culture The beliefs and practices of small, homogenous groups of people, often living in rural areas that are relatively isolated and slow to change, are known as folk cultures. Like all cultures, they demonstrate the diverse ways that people have adapted to a physical environment. For example, people around the world learned to make shelters out of available resources, whether 3.1: INTRODUCTION TO CULTURE 133 it was snow or mud bricks or wood. However, people used similar resources such as wood differently. In Scandinavia, people used trees to build cabins. In the American Midwest, people processed trees into boards, built a frame, and attached the boards to it. Many traits of folk culture continue today. Corn was first grown in Mexico around 10,000 years ago, and it is still grown there today. While many elements of folk culture exist side by side with modern culture, there are people whose societies have changed little, if at all, from long ago. These people practice traditional cultures, those which have not been affected by modern technology or influences. They often live in remote regions, such as some small tribes in the Amazon rainforest, and have scant knowledge of the outside world. As the lines continue blurring between cultural designations, the Amish of Pennsylvania are often referenced as both folk and traditional culture. Indigenous Culture When members of an ethnic group reside in their ancestral lands, and typically possess unique cultural traits, such as speaking their own exclusive language, they are considered an indigenous culture. Some indigenous peoples have been displaced from their native lands, but still practice their indigenous culture. Native Americans in the United States, such as the Navajo, have kept indigenous cultural practices. First Nations of Canada, such as the Inuit, have also retained their indigenous culture. Globalization and Popular Culture As a result of the Industrial Revolution, improvements in transportation and communication have shortened the time required for movement, trade, or other forms of interaction between two places. This development, known as space-time compression (see Topics 1.4 and 3.6), has accelerated culture change around the world. In 1817, a freight shipment from Cincinnati needed 52 days to reach New York City. By 1850, because of canals and railroads, it took half that long. And by 1852, it took only 7 days. Today, an airplane flight takes only a few hours, and digital information takes seconds or less. Similar change has occurred on the global scale. People travel freely across the world in a matter of hours, and communication has advanced to a point where people share information instantaneously across the globe. The increased global interaction has had a profound impact on cultures, from spreading English across the world to instant sharing of news, events and music. Globalization specifically refers to the increased integration of the world economy since the 1970s. The process of intensified interaction among peoples, governments, and companies of different countries around the globe has had profound impacts on culture. The culture of the United States is intertwined with globalization. Through the influence of its corporations, Hollywood movies, and government, the United States exerts widespread influence in other countries. But other countries also shape American culture. For example, in 2019, the National Basketball Association included players from 38 countries or territories. When cultural traits- such as clothing, music, movies, and types of 134 HUMAN GEOGRAPHY: AP. EDITION businesses-spread quickly over a large area and are adopted by various groups, they become part of popular culture. Elements of popular culture often begin in urban areas and diffuse quickly through globalization processes such as the media and Internet. These elements can quickly be adopted worldwide, making them part of global culture. People around the world follow European soccer, Indian Bollywood movies, and Japanese animation known as anime. With people in many nations wearing similar clothes, listening to similar music, and eating similar food, popular cultural traits often promote uniformity in beliefs, values, and the cultural landscape across many places The cultural landscape, also known as the built environment (see Topic 3.2), is the modification of the environment by a group and is a visible reflection of that group's cultural beliefs and values. Traditional Culture to Popular Culture Popular culture emphasizes trying what is new rather than preserving what is traditional. Many people, especially older generations or those who follow a folk culture, openly resist the adoption of popular cultural traits. They do this by preserving traditional languages, religions, values, and foods. While older generations often resist the adoption of popular culture, they seldom are successful in keeping their traditional cultures from changing, especially among the young people of their society. One clash between popular and traditional culture is occurring in Brazil. As the population expands to the interior of the rain forest, many indigenous cultures, like the Yanamamo tribe, have more contact with outside groups. Remaining isolated by the forest is becoming increasingly difficult as many young people from the indigenous cultures become exposed to popular culture and begin to integrate into the larger Brazilian society. As the young people leave their communities, they are more likely to accept popular culture at the expense of their indigenous cultural heritage, which threatens the very existence of their folk culture. Traditional culture typically exhibits horizontal diversity, meaning each traditional culture has its own customs and language that makes it distinct from other culture groups. Yet, people people within each group are usually homogeneous, or very similar to each other. By contrast, popular culture typically exhibits vertical diversity, meaning that modern urban societies are usually heterogeneous, or exhibiting differences, within the society and usually contain numerous multiethnic neighborhoods. However, on a global scale popular cultures are relatively similar with the same type of malls, shops, fast food, and clothing. Urban global culture centers are not identical, yet, global cities often do not have as much horizontal diversity across space as folk cultures. 3.1: INTRODUCTION TO CULTURE 135 COMPARING TRADITIONAL AND POPULAR CULTURE Trait Traditional Culture Popular or Global Culture Society • Rural and isolated location • Urban and connected location • Homogeneous and • Diverse and multiethnic indigenous population population • Most people speak an • Many people speak a global indigenous or ethnic local language such as English or language Arabic • Horizontal diversity • Vertical diversity Social • Emphasis on community and • Emphasis on individualism and Structure conformity making choices • Families live close to each • Dispersed families other • Weakly defined gender roles • Well-defined gender roles Diffusion • Relatively slow and limited • Relatively rapid and extensive • Primarily through relocation • Often hierarchical • Oral traditions and stories • Social media and mass media Buildings and • Materials produced locally, • Materials produced in distant Housing such as stone or grass factories, such as steel or glass • Built by community or owner • Built by a business • Similar style for community • Variety of architectural styles • Different between cultures • Similar between cities • Traditional architecture • Postmodern / contemporary architecture Food • Locally produced • Often imported • Choices limited by tradition • Wide range of choice • Prepared by the family or • Purchased in restaurants community Spatial Focus • Local and regional • National and global Artifacts, Mentifacts, and Sociofacts Whether a cultural attribute is considered traditional, folk, indigenous, or popular in nature, it is valuable to differentiate between elements of culture that can be seen and those that can not. There are artifacts that comprise the material culture, which consists of tangible things, or those that can be experienced by the senses. Art, clothing, food, music, sports, and housing types are all tangible elements of culture. Another element of the study of artifacts is understanding the techniques to use or build a specific artifact. Artifacts can be unique to a particular culture, or can be shared. For example, people of all cultures need to communicate through language, yet there are many groups that possess languages unique to their culture. The ability to read, write and understand the English language is an artifact of importance for much of popular global culture. 136 HUMAN GEOGRAPHY: AP" EDITION Mentifacts comprise a group's nonmaterial culture and consist ofintangible concepts, or those not having a physical presence. Beliefs, values, practices, and aesthetics (pleasing in appearance) determine what a cultural group views as acceptable and desirable. Mentifacts can also be unique or shared. People of many cultures possess an belief in one or many deities, and often the deities are unique to that culture. The belief in a god is a mentifact-the religious building or symbols are artifacts. Cultural groups also possess sociofacts, which are the ways people organize their society and relate to one another. Taken altogether, people tend to see the whole of their culture as greater than the sum of its individual parts. Sociofacts are embodied through families, governments, sports teams, religious organizations, education systems, and other social constructs. As with artifacts and mentifacts, sociofacts may also be unique or similar to other societies. Families are the foundations of most societies, yet what constitutes the structure of a family may vary widely between cultural groups. For example, Western cultures tend to view the nuclear family, consisting of the parents and their children as the basic family unit. By contrast, in many Western African cultures the norm is the extended family, consisting of several generations and other family members such as cousins living under one roof.

Cells of different organisms and even cells within the same organism are very diverse in terms of shape, size, and internal organization. One theme that occurs again and again throughout biology is that form follows function. In other words, a cell’s function influences its physical features. Cell Shape The diversity in cell shapes reflects the different functions of cells. Compare the cell shapes shown in Figure 4-4. The long extensions that reach out in various directions from the nerve cell shown in Figure 4-4a allow the cell to send and receive nerve impulses. The flat, platelike shape of skin cells in Figure 4-4b suits their function of covering and protecting the surface of the body. As shown below, a cell’s shape can be simple or complex depending on the function of the cell. Each cell has a shape that has evolved to allow the cell to perform its function effectively. SECTION 2 OBJECTIVES ● Explain the relationship between cell shape and cell function. ● Identify the factor that limits cell size. ● Describe the three basic parts of a cell. ● Compare prokaryotic cells and eukaryotic cells. ● Analyze the relationship among cells, tissues, organs, organ systems, and organisms. VOCABULARY plasma membrane cytoplasm cytosol nucleus prokaryote eukaryote organelle tissue organ organ system Cells have various shapes. (a) Nerve cells have long extensions. (b) Skin cells are flat and platelike. (c) Egg cells are spherical. (d) Some bacteria are rod shaped. (e) Some plant cells are rectangular. FIGURE 4-4 (a) Nerve cell (b) Skin cells (c) Egg cell (d) Bacterial cells (e) Plant cells Copyright © by Holt, Rinehart and Winston. All rights reserved. 1. All cubes have volume and surface area. The total surface area is equal to the sum of the areas of each of the six sides (area = length X width). 2. If you split the first cube into eight smaller cubes, you get 48 sides. The volume remains constant, but the total surface area doubles. 3. If you split each of the eight cubes into eight smaller cubes, you have 64 cubes that together contain the same volume as the first cube. The total surface area, however, has doubled again. CELL STRUCTURE AND FUNCTION 73 Cell Size Cells differ not only in their shape but also in their size. A few types of cells are large enough to be seen by the unaided human eye. For example, the nerve cells that extend from a giraffe’s spinal cord to its foot can be 2 m (about 6 1/2 ft) long. A human egg cell is about the size of the period at the end of this sentence. Most cells, how- ever, are only 10 to 50 μm in diameter, or about 1/500 the size of the period at the end of this sentence. The size of a cell is limited by the relationship of the cell’s outer surface area to its volume, or its surface area–to-volume ratio. As a cell grows, its volume increases much faster than its surface area does, as shown in Figure 4-5. This trend is important because the materials needed by a cell (such as nutrients and oxygen) and the wastes produced by a cell (such as carbon dioxide) must pass into and out of the cell through its surface. If a cell were to become very large, the volume would increase much more than the surface area. Therefore, the surface area would not allow materials to enter or leave the cell quickly enough to meet the cell’s needs. As a result, most cells are microscopic in size. Comparing Surface Cells Materials microscope, prepared slides of plant (dicot) stem and ani- mal (human) skin, pencil, paper Procedure Examine slides by using medium magnification (100). Observe and draw the sur- face cells of the plant stem and the animal skin. Analysis How do the surface cells of each organism differ from the cells beneath the surface cells? What is the function of the surface cells? Explain how surface cells are suited to their function based on their shape. Quick Lab Small cells can exchange substances more readily than large cells because small objects have a higher surface area–to-volume ratio. FIGURE 4-5 mb06se_csfs02.qxd 5/18/07 10:54 AM Page 73 74 CHAPTER 4 BASIC PARTS OF A CELL Despite the diversity among cells, three basic features are common to all cell types. All cells have an outer boundary, an interior sub- stance, and a control region. Plasma Membrane The cell’s outer boundary, called the plasma membrane (or the cell membrane), covers a cell’s surface and acts as a barrier between the inside and the outside of a cell. All materials enter or exit through the plasma membrane. The surface of a plasma mem- brane is shown in Figure 4-6a. Cytoplasm The region of the cell that is within the plasma membrane and that includes the fluid, the cytoskeleton, and all of the organelles except the nucleus is called the cytoplasm. The part of the cytoplasm that includes molecules and small particles, such as ribosomes, but not membrane-bound organelles is the cytosol. About 20 percent of the cytosol is made up of protein. Control Center Cells carry coded information in the form of DNA for regulating their functions and reproducing themselves. The DNA in some types of cells floats freely inside the cell. Other cells have a mem- brane-bound organelle that contains a cell’s DNA. This membrane- bound structure is called the nucleus. Most of the functions of a eukaryotic cell are controlled by the cell’s nucleus. The nucleus is often the most prominent structure within a eukaryotic cell. It maintains its shape with the help of a protein skeleton called the nuclear matrix. The nucleus of a typical animal cell is shown in

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