PO WER - XX LO Gdańsk - Pythagoras - mathematical problems
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The document discusses the sum of angles in a triangle, the Pythagorean theorem for calculating the hypotenuse of a right triangle, and how to calculate the arithmetic average or mean of a data set. It provides an example of calculating the unknown angle Y in a triangle where X=40 and Z=70, and calculating the average of the numbers 2, 4, 5, 6, 8, 9, 11, 13, 23. Key terms are defined in Polish including angle, triangle, hypotenuse, divide, and average/mean.
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This document discusses several geometry theorems:
- The Basic Proportionality Theorem (also known as Thales' Theorem) states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.
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A triangle is a three-sided polygon with three vertices and edges. It is one of the basic shapes in geometry. A triangle is denoted by listing the vertices as △ABC. The document discusses different types of triangles and their properties in Euclidean geometry. It defines a parallelogram as a quadrilateral with two pairs of parallel sides, where opposite sides are equal in length and opposite angles are equal in measure. The document also provides the formulas for calculating the area of both triangles and parallelograms by multiplying the base by the height.
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This document provides instruction on similarity in right triangles. It begins with examples of identifying similar right triangles and finding geometric means. Geometric mean is defined as the positive square root of the product of two numbers. The document then shows how geometric means can be used to find unknown side lengths in right triangles using proportions. Examples demonstrate applications to measurement problems. The lesson concludes with a quiz reviewing key concepts like writing similarity statements and using proportions with geometric means to solve for missing side lengths in right triangles.
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This document summarizes key concepts in geometry related to triangles. It discusses similarity criteria including AAA, SSA, and SSS. It also covers the area theorem, Pythagorean theorem, and its converse. The basic proportionality theorem and its converse are explained as well as how they relate to parallel lines. In summary, this document outlines important triangle properties and theorems for understanding similarity, area, right triangles, and parallel lines.
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This document discusses three rules for determining if triangles are similar: the AA Similarity Postulate, SAS Similarity Theorem, and SSS Similarity Theorem. It provides examples of applying each rule to determine if triangles are similar, and if so, writing the similarity statement and ratio.
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- There are four similarity criteria: AAA, SAS, SSS, and ASA, which define conditions for when two triangles are similar.
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This document provides instruction on similarity in right triangles. It begins with examples of identifying similar right triangles and finding geometric means. Geometric mean is defined as the positive square root of the product of two numbers. The document then shows how geometric means can be used to find unknown side lengths in right triangles using proportions. Examples demonstrate applications to measurement problems. The lesson concludes with a quiz reviewing key concepts like writing similarity statements and using proportions with geometric means to solve for missing side lengths in right triangles.
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- A parallelogram is a quadrilateral with two pairs of parallel sides, and opposite angles and sides of equal measure. The area of a parallelogram is calculated as the base multiplied by the height.
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This document discusses ways to prove that two lines are parallel using postulates and theorems about angles formed when lines are cut by a transversal. Specifically, it states that two lines are parallel if:
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- A parallelogram is a quadrilateral with two pairs of parallel sides, and opposite angles and sides of equal measure. The area of a parallelogram is calculated as the base multiplied by the height.
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Mathematics can be divided into several branches that each focus on different areas of study. Some of the main branches include arithmetic, algebra, mathematical analysis, combinatorics, and geometry/topology. Arithmetic is the oldest branch and focuses on numbers and basic operations like addition and multiplication. Algebra studies the properties of numbers and methods for solving equations. Mathematical analysis examines continuous change through calculus, limits, and functions. Combinatorics analyzes discrete collections of objects and their relationships. Geometry and topology use spatial relationships and properties of shapes.
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The survey analyzed the positive impacts of participants in an Erasmus+ project called "EAT, COMPETE, GET FIT" at a school in Gdańsk, Poland. Most participants had not previously taken part in an EU project. The majority agreed that the project helped them learn about healthy living, balanced diets, and topics like nutrition, obesity, and Polish traditional dishes. Eighty-two percent reported learning interesting facts about Gdańsk and healthy lifestyles. While most improved their teamwork skills and found other presentations useful, nine students realized they feel stressed when presenting publicly. Overall, the project effectively increased awareness of healthy lifestyle choices.
Results of tobacco use survey in XX LO Gdańsk
A survey was conducted of students at a high school in Gdansk, Poland about tobacco use. The key findings were:
1) 6% of respondents currently smoke, with most of those smokers not having tried to quit. The top reasons non-smokers gave for not smoking were that they think it is unhealthy and do not like the smell/taste.
2) 67% of respondents said close relatives smoke, and 76% said the smell of cigarettes bothers them. The most common reasons for smoking were that it is relaxing and people feel addicted or stressed.
3) When asked about smoking-related illnesses, 89 respondents cited cancer and 1 cited asthma. Most respondents supported bans on
Erasmus + Hungary, XX LO Gdańsk
During a school mobility program in Hungary from the 18th to the 24th of March, students from Poland visited various locations to learn about health, first aid, and Hungarian culture. On the first day, they toured their host school and Hungarian classrooms, and presented on their home countries. They learned first aid, baby care, and blood pressure measurement from Hungarian students. Later they visited a hospital and had dinner and a tour there. On the second day, they presented on healthcare systems and learned useful Hungarian words. They visited an ambulance station and prepared traditional foods from their countries. They went to a farm and had Hungarian goulash. The third day involved a guided tour of the Hungarian Parliament and exploring Budapest. They also
PO WER - XX LO Gdańsk - Vieta's formulas
This document discusses Vieta's formula, which relates the coefficients of polynomials to the sums and products of their roots. It provides the definition of Vieta's formula and multiple examples to illustrate it. The document was created by Antoni and Piotr.
PO WER - XX LO Gdańsk - Francois Viete - mathematical problems
Francois Viete was a 16th century French mathematician who made important contributions to algebra. He introduced systematic use of letters as symbols in algebra, formulated formulas for solving quadratic equations, and was an adviser to French kings. He also worked as a teacher and helped break enemy codes during wars between France and Spain.
PO WER - XX LO Gdańsk - Why is our environment important?
The document discusses why the environment is important. It explains that the environment is where humans live and get resources for survival. All living things on Earth are connected through food chains, with the sun providing energy that plants use and animals consume plants or each other. Within the global biosphere, smaller ecosystems like rainforests and deserts interact; problems in one area affect the whole planet. However, environmental degradation through pollution and overuse of resources like water and fossil fuels endangers these systems. Protecting the environment is important because Earth is the only home humans have.
PO WER - XX LO Gdańsk - Environment protection
National parks, nature parks, natural monuments, and nature reserves help protect Poland's environment. National parks cover large areas of at least 1,000 hectares and protect all natural and landscape values. Nature parks preserve areas for their natural, historical, cultural, and landscape values. Natural monuments include single trees, bushes, groups of trees, and geological formations. Together these designations help conserve Poland's natural resources and biodiversity.
PO WER - XX LO Gdańsk - Let's save the Earth
China produces over 50% of the world's textiles but is also the largest polluter and carbon emitter. Water pollution in rural areas of China does not meet basic safety standards. An artist created images to bring attention to pollution's effects on oceans. Over 100 years, pollution has degraded the Baltic Sea through drainage, industrialization, urban development and sewage. Air pollution kills over 3 million people annually from diseases like Beijing cough. A WHO report found that only 6 of 65 Polish cities met air quality standards, with Krakow being the most polluted and Gdansk the cleanest. Pollution can contaminate drinking water supplies and kill beneficial species, and air pollution worsens global warming. Small actions like using less
PO WER - XX LO Gdańsk - Environmental protection
Environmental protection involves practices that protect the natural environment for both nature and humans. Air pollution from energy production and industry is a major threat, releasing pollutants like sulfur dioxide, nitrogen oxides, and carbon dioxide. These pollutants are absorbed by humans and plants and can cause health issues while also contributing to acid rain and climate change. Reducing pollution requires low emission technologies as well as individual efforts to conserve resources and produce less waste.
PO WER - XX LO Gdańsk - Environmental protection in Pomerania Province
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like anxiety and depression.
PO WER - XX LO Gdańsk - Mathematics and treatment of cancer
Mathematics and statistical modeling can provide benefits for cancer treatment. Mathematical models of cancer processes can help researchers better understand the underlying biological mechanisms. Models can also be used to simulate disease progression and optimize therapeutic procedures. For example, models of cancer invasion describe processes like tumor cell migration, growth, and degradation of tissue. Additionally, 3D mathematical models present a three-dimensional image of the genome and allow simulations to be performed, providing insights into cancer development. Overall, the synergy between mathematics and biology can lead to more accurate applications and improved cancer therapies.
PO WER - XX LO Gdańsk - Electricity in biology - UG
In May, a class visited the University of Gdańsk for a biology lesson. They conducted experiments about electricity in the human body. The students measured electric current on their skin and learned about Ohm's law. They used equipment like an electrostatic machine. The class also learned about Luigi Galvani's experiments with frog legs in 1780 that discovered tension and potential in dead animals. Some fish can generate 300-600 volts of electricity to hunt, kill prey, or communicate. The students measured their blood pressure, sweating, and temperature in response to stimuli. One student received a mild electric shock that caused their thumb to shake uncontrollably. The lesson provided hands-on experiments to help students understand
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PO WER - XX LO Gdańsk - Pythagoras - mathematical problems
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