Geometry 3.3
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This document discusses parallel lines and transversals. It defines corresponding angles, alternate exterior angles, alternate interior angles, and consecutive angles as being congruent when two parallel lines are cut by a transversal. It provides examples problems involving finding missing angle measures using these properties. Students are asked to solve additional problems by identifying the specific corresponding, alternate, or consecutive angle pairs and stating the property that proves the angles are congruent.
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1. The document provides information about polygons, including definitions of terms like convex polygon and regular polygon.
2. Formulas are given for calculating the sum of interior angles of polygons with n sides (180(n-2)) and the measure of one interior and one exterior angle of regular polygons.
3. Examples are provided of applying these formulas to specific polygons like triangles and squares.
2.7.1 Properties of Polygons
1) Polygons are named based on the number of sides, such as triangles having 3 sides and quadrilaterals having 4 sides.
2) The interior angles of polygons can be classified as regular, equilateral, equiangular or concave/convex based on the shape of the angles.
3) The sum of the interior angles of any convex polygon is (n-2)×180°, where n is the number of sides, and the sum of the exterior angles is always 360° for any convex polygon.
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There are four types of angles: acute, obtuse, right and reflex. Angle properties include: angles at a point add to 360 degrees; angles on a straight line add to 180 degrees; vertically opposite angles are equal; corresponding angles and alternate interior angles of parallel lines are equal; interior angles of a triangle add to 180 degrees; exterior angle of a triangle equals the sum of the interior opposite angles; interior angles of polygons add up based on the number of sides, following the formula (n-2) x 180 degrees, where n is the number of sides. Regular polygons have equal interior angles that add up to the total interior angle based on the number of sides.
Obj. 25 Properties of Polygons
Name polygons based on their number of sides
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The document discusses interior and exterior angles of polygons. It states that the sum of the interior angles of any convex n-gon is (n-2) * 180 degrees. The sum of the exterior angles of any convex n-gon is always 360 degrees. Examples are provided to demonstrate using these formulas to find missing angle measures in different polygons. The key points are that the interior angle sum is (n-2) * 180 and the exterior angle sum is always 360.
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Identify and name polygons based on their number of sides, and whether they are concave or convex, and whether they are equilateral, equiangular, or regular.
Calculate the measures of interior and exterior angles of polygons.
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The document discusses angle measures in polygons:
- The sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees.
- For a regular polygon with n sides, the measure of each interior angle is (n-2) * 180 / n degrees.
- The sum of the exterior angles of any polygon is always 360 degrees.
- Examples are provided to demonstrate calculating interior and exterior angle measures for different regular polygons.
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2. Formulas are given for calculating the sum of interior angles of polygons with n sides (180(n-2)) and the measure of one interior and one exterior angle of regular polygons.
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The document discusses interior and exterior angles of polygons. It states that the sum of the interior angles of any convex n-gon is (n-2) * 180 degrees. The sum of the exterior angles of any convex n-gon is always 360 degrees. Examples are provided to demonstrate using these formulas to find missing angle measures in different polygons. The key points are that the interior angle sum is (n-2) * 180 and the exterior angle sum is always 360.
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environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
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The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
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'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
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Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
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Geometry 3.3
- 1. 3.3: Parallel Lines and Transversals
- 2. Goals • Use properties of parallel lines to solve problems
- 3. Special Angles formed by Parallel Lines and Transversals Corresponding Angles: F, Alternate Exterior Angles: like vertical angles, Alternate Interior Angles: Z, Consecutive Angles: C, supplementary ≅ ≅ ≅
- 4. Ex. 1:
- 6. Your Turn # 1:: (a) (b)
- 7. Your Turn # 1:: (a) 113yx exterioralternate:y&x 113x 67-180x 180x67 pairlinear:xand67 == = = =+
- 8. Your Turn # 1:: (b) 90y interioralternate:y&90 90x 90-180x 180x90 angleseconsecutiv:x&90 90angleright = = = =+ =
- 9. Your Turn # 2: (a) (b)
- 10. Your Turn # 2: (a) y y y = = = 23 5 5 5 115 5115 :anglesexterioralternate
- 11. Your Turn # 2: (b) 7 13 91 13 13x 9113x 89-18013x89-89 18013x89 18013x5-94 1805)-(13x94 angleseconsecutiv--anglesVertical = = = =+ =+ =+ =+ > x
- 12. SW 3.3 Draw the picture, and justify your answer by stating the angle pair formed. p. 146: # 8, 10, 12, 14, 16, 18, 20, 22, 24, 26