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Central Angles in circles
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Solving Problems Involving Central Angles, Inscribed Angles, and angles Formed by Two Intersecting Chords in Circles
CENTRAL AND INSCRIBE ANGLES, INTERIOR AND EXTERIOR ANLES IN A CIRCLE, MINOR AND MAJOR ARC, SECANTS, TANGENTS AND SEGMENTS
Short Quiz in Math 10 derives inductively the relations among chords, arcs, central angles,
Short Quiz in Math 10 proves theorems related to chords, arcs, central angles, and inscribed
Create a quiz from this information: 1. WOOD CARVING - woodworking using a cutting tool in one hand (Chisel & mallet) β’ Woodcarvers: a. Ifugao 1. Bul-ul 2. Lingling-o 3. Hagabi b. Tagbanua (Central and Northern Palawan ) c. Maranao (Lanao del Sur) - uses the okir motif = curvilinear d. Paete (Paete, Laguna) - center of woodcarving in the Philippines 2. POTTERY - forming vessels with clay & other ceramic materials which are fired at high temperatures to give them a hard, durable form. - longest traditions in Philippine art. - Vessels for holding food/liquids, decorations, sculptures. 3. FABRIC WEAVING - textile production in which two distinct sets of yarns or threads are interlaced at right angles to form a fabric or cloth. - Textile hand-weaving = most attractive and interesting traditional crafts of the Philippines. - Uses a tradtional machine = Loom β’ Example of Indigenous Woven Fabrics in the Philippines 1. Hablon 2. Kalinga Textiles 3. Mabal Tabih 4. Bagobo Inabal 4. BASKETRY - art of making baskets through weaving or braiding - from bamboo or seagrasses - The spokes or stakes are the foundation of a basket β’ Techniques 1. Paiting 2. Twining 3. Wicker 4.Coling
The cytoskeleton is a network of thin tubes and filaments that crisscrosses the cytosol. The tubes and filaments give shape to the cell from the inside in the same way that tent poles support the shape of a tent. The cytoskeleton also acts as a system of internal tracks, shown in Figure 4-18, on which items move around inside the cell. The cytoskeletonβs functions are based on several struc- tural elements. Three of these are microtubules, microfilaments, and intermediate filaments, shown and described in Table 4-2. Microtubules Microtubules are hollow tubes made of a protein called tubulin. Each tubulin molecule consists of two slightly different subunits. Microtubules radiate outward from a central point called the centrosome near the nucleus. Microtubules hold organelles in place, maintain a cellβs shape, and act as tracks that guide organelles and molecules as they move within the cell. Microfilaments Finer than microtubules, microfilaments are long threads of the beadlike protein actin and are linked end to end and wrapped around each other like two strands of a rope. Microfilaments con- tribute to cell movement, including the crawling of white blood cells and the contraction of muscle cells. Intermediate Filaments Intermediate filaments are rods that anchor the nucleus and some other organelles to their places in the cell. They maintain the inter- nal shape of the nucleus. Hair-follicle cells produce large quantities of intermediate filament proteins. These proteins make up most of the hair shaft. 84 CHAPTER 4 TABLE 4-2 The Structure of the Cytoskeleton Property Microtubules Microfilaments Intermediate filaments Structure hollow tubes made of two strands of intertwined protein fibers coiled into coiled protein protein cables Protein subunits tubulin, with two subunits: Γ₯ actin one of several types of and β« tubulin fibrous proteins Main function maintenance of cell shape; cell maintenance and changing of maintenance of cell shape; motility (in cilia and flagella); cell shape; muscle contraction; anchor nucleus and other chromosome movement; movement of cytoplasm; cell organelles; maintenance of organelle movement motility; cell division shape of nucleus Shape Microtubules provide a path for organelles and molecules as they move throughout the cell. FIGURE 4-18 Microtubules Nucleus Endoplasmic reticulum Mitochondrion Ribosomes Copyright Β© by Holt, Rinehart and Winston. All rights reserved. Copyright Β© by Holt, Rinehart and Winston. All rights reserved. CELL STRUCTURE AND FUNCTION 85 1. Explain how the fluid mosaic model describes the plasma membrane. 2. List three cellular functions that occur in the nucleus. 3. Describe the organelles that are found in a eukaryotic cell. 4. Identify two characteristics that make mitochon- dria different from other organelles. 5. Contrast three types of cytoskeletal fibers. CRITICAL THINKING 6. Relating Concepts If a cell has a high energy requirement, would you expect the cell to have many mitochondria or few mitochondria? Why? 7. Analyzing Information How do scientists think that mitochondria originated? Why? 8. Analyzing Statements It is not completely accurate to say that organelles are floating freely in the cytosol. Why not? SECTION 3 REVIEW During cell division, centrioles organize microtubules that pull the chromosomes (orange) apart. The centrioles are at the center of rays of microtubules, which have been stained green with a fluorescent dye. FIGURE 4-20 Cilia and Flagella Cilia (SIL-ee-uh) and flagella (fluh-JEL-uh) are hairlike structures that extend from the surface of the cell, where they assist in movement. Cilia are short and are present in large numbers on certain cells, whereas flagella are longer and are far less numerous on the cells where they occur. Cilia and flagella have a membrane on their outer surface and an internal structure of nine pairs of micro- tubules around two central tubules, as Figure 4-19 shows. Cilia on cells in the inner ear vibrate and help detect sound. Cilia cover the surfaces of many protists and βrowβ the protists through water like thousands of oars. On other protists, cilia sweep water and food particles into a mouthlike opening. Many kinds of protists use flagella to propel themselves, as do human sperm cells. Centrioles Centrioles consist of two short cylinders of microtubules at right angles to each other and are situated in the cytoplasm near the nuclear envelope. Centrioles occur in animal cells, where they organize the microtubules of the cytoskeleton during cell division, as shown in Figure 4-20. Plant cells lack centrioles. Basal bodies have the same structure that centrioles do. Basal bodies are found at the base of cilia and flagella and appear to organize the devel- opment of cilia and flagella.
Q1. A teacher designs a lesson where students compute real-life percentages such as discounts and savings. π 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. π What is the GCF of 24 and 36? A. 6 B. 8 C. 12 D. 18 π FRACTIONS, DECIMALS, AND POWERS Q3. A learner converts fractions into percentages for data interpretation. π 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. π What is the value of 252^525? A. 25 B. 30 C. 32 D. 64 π ALGEBRA (EQUATIONS AND EXPRESSIONS) Q5. A teacher guides students to solve equations that represent real-life situations. π 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. π Simplify: 3(x+4)β2x3(x + 4) - 2x3(x+4)β2x A. x + 12 B. x + 4 C. 5x + 4 D. 5x + 12 π FUNCTIONS AND GRAPHING Q7. A student analyzes a linear equation to determine its rate of change. π What is the slope of y=3xβ5y = 3x - 5y=3xβ5? A. -5 B. -3 C. 3 D. 5 Q8. A learner evaluates functions to predict outcomes. π 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 π GEOMETRY Q9. Students explore geometric shapes and their properties through visual models. π What is the sum of interior angles of a triangle? A. 90Β° B. 180Β° C. 270Β° D. 360Β° Q10. A student calculates the area of a classroom table with dimensions 8 cm by 5 cm. π What is the area? A. 26 sq cm B. 30 sq cm C. 40 sq cm D. 48 sq cm π MEASUREMENT AND FIGURES Q11. A learner determines the volume of a cube used in a science experiment. π 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. π How many sides does a hexagon have? A. 5 B. 6 C. 7 D. 8 π STATISTICS AND PROBABILITY Q13. A teacher helps students interpret data sets using measures of central tendency. π 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. π What is the probability of getting heads? A. 1/4 B. 1/3 C. 1/2 D. 2/3 π WORD PROBLEMS (APPLICATION) Q15. A car travels 180 km in 3 hours during a learning task on speed. π 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. π 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. π 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. π 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. π What is the simple interest on β±1000 at 5% for 2 years? A. β±50 B. β±75 C. β±100 D. β±150 Q20. A learner solves a perimeter problem involving a rectangle. π 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 β
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Central angles, inscribed angles, and intercepted arcs