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Aryabhata was an Indian mathematician and astronomer born in 476 CE in Patna, India who made early contributions to trigonometry and developed concepts of sine, cosine, and versine. Some of his key
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This document defines and classifies different types of quadrilaterals. It introduces quadrilaterals and defines special types including parallelograms, rectangles, rhombuses, squares, and trapezoids. Quadrilaterals can have multiple names because some properties overlap between types. The best name is the most specific one. The document shows how the types are related through Venn diagrams and concept maps, and provides examples of classifying quadrilaterals and identifying the best name.
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Proves theorems on the different kinds of parallelogram.pptx
This document provides information about different types of parallelograms - rectangles, rhombuses, and squares. It defines their key properties and includes theorems about each type. Theorems discussed include: if a parallelogram has a right angle it is a rectangle; the diagonals of a rectangle are congruent; in a rhombus the diagonals are perpendicular and bisect each other; and the diagonals of a square bisect each other, are congruent and perpendicular. Examples are also provided to demonstrate applying the theorems.
QUADRILATERALS.pptx
The document provides information about different types of quadrilaterals:
- A quadrilateral is a plane shape with four sides and four angles at each vertex. There are several types of quadrilaterals classified by their properties.
- Parallelograms have two pairs of parallel sides and their opposite angles are congruent. Special types of parallelograms include rectangles, rhombi, and squares.
- Trapezoids have exactly one pair of parallel sides, while kites have two pairs of congruent adjacent sides. Properties and definitions of each shape are described.
- The median and altitude of a trapezoid are defined. Isosceles and right trapezoids are subtypes
Geovocab
This document defines and provides examples of geometric shapes and their properties. It discusses polygons like triangles and quadrilaterals, describing their classifications based on sides or angles. It also defines three-dimensional shapes like prisms, pyramids, cylinders, and cones, noting properties like parallel bases and lateral faces. Key properties discussed include symmetry, parallelism of sides, congruence of sides and angles, and right angles.
BASICS OF QUADRILATERALS
This document defines and describes different types of quadrilaterals. It begins by defining a quadrilateral as a figure with four sides and four angles. It then defines key terms like adjacent sides. The main types of quadrilaterals discussed are trapezium, kite, rhombus, square, parallelogram, and rectangle. Each shape is defined, such as a rectangle having four right angles and parallel opposite sides. Properties of different quadrilaterals are also covered, like diagonals bisecting each other in a rhombus. In the end, it states the angle sum property that the interior angles of any quadrilateral sum to 360 degrees.
Q2M1-4.pptx
This document discusses different types of quadrilaterals including their definitions and properties. It defines a quadrilateral as a four-sided polygon and introduces various terms used to describe quadrilateral parts such as sides, angles, and diagonals. It then presents different types of quadrilaterals in a family tree showing their relationships and provides detailed definitions and properties for parallelograms, rhombuses, rectangles, and squares. The document concludes with an example problem involving finding measurements of a parallelogram using its properties.
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rvderRFVERVGERVDFTYREWERTYUJIKLPKJHGFDSDFGHJKL;KJHGFDSDRTYUIOKJHGFDSAERTYUIOKJHGFDSE567IOPLKJNBVFDSW34RTYUIKJHGFDSEDRTYUIOKJNBVCXSERTYUIOLKMJNBVCDXSASERTYUIOL;KJNBHGVFDSD
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Triangles can be classified based on the number of congruent sides. There are three types of triangles: scalene (no congruent sides), isosceles (at least two congruent sides), and equilateral (three congruent sides). Heron's formula provides a way to calculate the area of any triangle using the lengths of its three sides. The formula is: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (sum of sides divided by 2). The document also presents a researched formula for calculating the area of an equilateral triangle using only the length of one side.
Original presentation
Euclid's Geometry outlines Euclid's influential work on geometry from around 300 BCE. It defines Euclidean geometry as the study of plane and solid figures using axioms and theorems. It also distinguishes between axioms, which are general mathematical assumptions, and postulates, which are specific geometric assumptions. Finally, it briefly discusses several influential mathematicians throughout history and their contributions, including Euclid, Ramanujan, Descartes, Aryabhatta, and Thales.
Quadrilaterals
This document provides information about various types of quadrilaterals (four-sided shapes). It defines quadrilateral, rectangle, rhombus, square, parallelogram, and trapezium. For each shape, it describes the key properties like side lengths, angle measures, and how to calculate the area and perimeter. The goal is to explain these geometric concepts in a clear, step-by-step manner to make mathematics more accessible and enjoyable for students.
Mathematics
This document discusses different types of triangles and their properties. It explains that all triangles have 3 sides and 3 angles that add up to 180 degrees. It also discusses the Triangle Inequality Theorem. Triangles are classified based on equal or unequal side lengths (scalene, isosceles, equilateral) and angle types (acute, right, obtuse). When combining these classifications, there are 7 possible triangle types. Examples and diagrams of each type are provided.
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Proves theorems on the different kinds of parallelogram.pptx
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- 4. Born 22 December 1887 Erode, Madras Presidency, British Raj(nowTamil Nadu, India) Died 26 April 1920 (aged 32) Kumbakonam, Madras Presidency,British Raj (nowTamil Nadu, India) Residence Kumbakonam, Madras Presidency Madras, Madras Presidency London, United Kingdom Nationality Indian Fields Mathematics Institutions Trinity College, Cambridge Alma mater Government Arts College (no degree) Pachaiyappa's College (no degree) Trinity College, Cambridge (BSc, 1916) Thesis Highly Composite Numbers (1916)
- 6. Born 476 CE Kusumapura (Pataliputra) (present day Patna[1] Died 550 CE Residence India Religion Hinduism Academic background Influences Surya Siddhanta Academic work Era Gupta era Main interests Mathematics, astronomy Notable works Āryabhaṭīya, Arya-siddhanta Notable ideas Explanation of lunar eclipse andsolar eclipse, rotation of Earth on its axis, reflection of light by moon,sinusoidal functions, solution of single variable quadratic equation,value of π correct to 4 decimal places, circumference of Earth to 99.8% accuracy, calculation of the length of sidereal year Influenced Lalla, Bhaskara I, Brahmagupta,Varahamihira
- 7. TYPE OF
- 8. Types of Quadrilaterals • A closed plane figure bounded by four straight lines is called a quadrilateral. • A quadrilateral has four vertices. • The line segments joining the opposite vertices are called its diagonals. • A quadrilateral has 4 angles. The sum of its interior angles is 360 ⁰. 8
- 9. • Parallelogram: If the line segments in each pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is called a parallelogram. • Rhombus: If all the sides of a parallelogram are congruent, then it is called a rhombus. 9
- 10. • Rectangle: If all the angles of a parallelogram are right angles, then the quadrilateral is called a rectangle. • Square: If all the sides of a rectangle are congruent, then it is called a square. • Trapezium: If in a quadrilateral, line segments in one pair of opposite side are parallel and the opposite sides in the other pair are not parallel, then the quadrilateral is called a trapezium. 10
- 11. Special Kinds of Quadrilaterals-kite • If in a quadrilateral, two pairs of adjacent sides are equal, then it is called a kite. • The diagonals of a kite are not equal but intersect each other at right angles. 11
- 12. You have learnt • A closed plane figure bounded by four straight lines is called a quadrilateral. • The sum of the interior angles of a quadrilateral is 360 ⁰. • If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. • If in a parallelogram, all sides are equal, then it is called a rhombus. • If in a parallelogram, one of the angles is a right angle, then it is called a rectangle. • If in a parallelogram, one of the angles is a right angle and all sided are equal, then it is called a square. 12