Polygon Notes
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The document defines and classifies polygons based on the number of sides. A polygon is a closed plane shape with three or more straight sides. Polygons are classified based on their number of sides, with specific names given to polygons with 3 to 12 sides, such as triangle, quadrilateral, pentagon, etc. Polygons can also be categorized as convex or concave based on whether the vertices point outward or inward. Regular polygons are those where all sides have the same length.
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1. The document defines and classifies different types of polygons, with a focus on quadrilaterals.
2. It describes properties of quadrilaterals including having four sides, four angles, one pair of diagonals, and the interior angle sum being 360 degrees.
3. Several specific types of quadrilaterals are defined, including rectangles, rhombus, squares, parallelograms, trapezoids, kites, and trapeziums. Their defining properties are provided.Understanding quadrilaterals chapter 3 NCERT 
Understanding quadrilaterals chapter 3 NCERT jai3077
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1. The document discusses different types of quadrilaterals including their definitions and properties.
2. Quadrilaterals are classified based on characteristics such as equal side lengths, parallel sides, right angles, and diagonals.
3. The main quadrilaterals discussed are rectangles, rhombus, squares, parallelograms, trapezoids, kites, and general quadrilaterals. Formulas for interior angle sums and relationships between different quadrilaterals are also provided.More from acavis (8)
Building Blocks Of Geometry
Building Blocks Of Geometryacavis
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The document discusses the basic building blocks of geometry - points, lines, and planes. It defines these terms and explains that while they cannot be strictly defined without circular references, they form the foundation for defining all other geometric concepts. Key terms like collinear, coplanar, line segments, rays, congruence, bisection, and parallel/perpendicular lines are then introduced and defined. The document also provides assumptions and limitations for interpreting geometric diagrams.The Geometry Of Solids Notes
The Geometry Of Solids Notesacavis
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The document discusses different types of geometric solids including polyhedrons, prisms, pyramids, spheres, cylinders and cones. It defines key terms used to describe and classify these shapes such as faces, edges, vertices, bases, lateral faces, radius and more. Regular polyhedrons have regular polygon faces that are all congruent, while prisms are polyhedrons with two congruent, parallel polygon bases connected by parallelogram faces. Pyramids have one polygon base and faces that meet at a vertex point. Spheres, cylinders and cones have curved surfaces rather than flat faces.Similar Triangles Notes
Similar Triangles Notesacavis
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1) Congruent and similar triangles can be used to simplify design and calculations. Congruent triangles have equal sides and angles, while similar triangles have the same shape but not necessarily the same size.
2) Corresponding sides and angles of similar triangles have the same ratios. Ratios can be used to determine unknown side lengths.
3) Triangles are similar if two angles are congruent (AA similarity) or if all three sides are proportional (SSS similarity).Pythagoras And The Pythagorean Theorem
Pythagoras And The Pythagorean Theoremacavis
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Pythagoras was a Greek mathematician born around 570 BCE in Samos, Greece. He founded a school in Croton, Italy where he studied mathematics and developed the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras made many contributions to mathematics and music. He discovered that the musical scale is based on string length ratios and ratios of whole numbers.Congruence Shortcuts Notes
Congruence Shortcuts Notesacavis
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Two triangles are congruent if they have the same size and shape. To prove triangles are congruent, it is sufficient to show that some corresponding parts, like sides or angles, are congruent. There are four main ways to prove triangles are congruent: side-angle-side (SAS), side-side-side (SSS), angle-side-angle (ASA), and angle-angle-side (AAS). Each involves showing that specific corresponding parts - two sides and an angle, three sides, two angles and a side, or two angles and a side - are congruent.Latitude, Longitude, And Scale
Latitude, Longitude, And Scaleacavis
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Latitude and longitude are coordinates that define locations on Earth. They are measured in degrees, minutes, and seconds, where degrees indicate lines on a map or globe, minutes are 1/60 of a degree, and seconds are 1/60 of a minute. Scale refers to the ratio of distances on a map compared to actual distances on Earth, such as 1 centimeter on a map representing 1 kilometer on the ground. It allows distances on maps to be measured and is constant throughout a given map or blueprint. Professions like mapmaking, engineering, and advertising use scale in their work.Logic Notes
Logic Notesacavis
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The document discusses different types of logical statements and their truth values. It defines simple and compound statements, truth tables, negation, conjunction, disjunction, implication, converse, and biconditional. Examples are provided to illustrate each concept, such as truth tables showing the possible truth value combinations of statements connected by logical operators like "and", "or", and "if-then".Fractals Notes
Fractals Notesacavis
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A fractal is a geometric figure that is self-similar, meaning it is exactly or approximately similar to its parts. Fractals are created using repeating patterns and include shapes like the Koch snowflake, Sierpinski triangle, Dragon Curve, and Mandelbrot set. Examples of fractals shown were the Koch snowflake, Sierpinski triangle and gasket, Cantor set, Dragon Curve, and Mandelbrot set.Polygon Notes
- 1. Polygons
- 2. What is a Polygon???? Any ideas? Write down what you think it is for #1.
- 3. A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).
- 4. Classifying Polygons by # of Sides 3 sided Polygon = Triangle Hint: Think Tricycle, tripod, Trilateration (Tri means 3)
- 5. Classifying Polygons by # of Sides 4 sided Polygon = Quadrilateral Hint: Think Quadrant, Quadruple, Quad (AKA 4-Wheeler)
- 6. Classifying Polygons by # of Sides 5 sided Polygon = Pentagon Hint: Think Pentathalon, or the government building The Pentagon
- 7. Classifying Polygons by # of Sides 6 sided Polygon = Hexagon Hint: Both Hexagon and Six have an x in them
- 8. Classifying Polygons by # of Sides 7 sided Polygon = Heptagon Hint: ???
- 9. Classifying Polygons by # of Sides 8 sided Polygon = Octagon Hint: octopus 8 legs
- 10. Classifying Polygons by # of Sides 9 sided Polygon = Nonagon Hint: Non is similar to Nine
- 11. Classifying Polygons by # of Sides 10 sided Polygon = Decagon Hint: Think Decade (10 years
- 12. Classifying Polygons by # of Sides 11 sided Polygon = Hendecagon Hint: ???
- 13. Classifying Polygons by # of Sides 12 sided Polygon = Dodecagon Hint: ???
- 14. Classifying Polygons by # of Sides Q: What do we call a polygon with more than 12 sides? A: An n-gon where n is the number of sides Ex: a 20 sided polygon is a 20-gon
- 15. Classifying Polygons by # of Sides # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Hendecagon 12 Dodecagon
- 16. Two Types of Polygons Convex all vertices point outward Concave at least one vertex points inward towards the center of the polygon (The side looks like it caved in)
- 17. Regular Polygons A Regular Polygon is a polygon in which all sides are the same length. Equilateral Triangle Square
- 18. Review of Similar Triangles 2 Triangles are similar if they have the same shape (i.e. the same angle in the same positions)
- 19. Similar Polygons The same is true of polygons. 2 polygons are similar if they have the same angles in the same positions (i.e. same shape) and the sides are proportional. ^ Similar Pentagons ^ Similar Trapezoids Similar Rectangles