Understanding quadrilaterals
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The document defines and classifies different types of quadrilaterals. It discusses properties of parallelograms, trapezoids, kites, and other quadrilaterals. Key types include parallelograms, which have two pairs of parallel sides, and trapezoids, which have one set of parallel sides. A square is defined as a special type of rectangle with four equal sides and four right angles. The document also discusses classifications of quadrilaterals based on angles and sides.
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- Parallelograms have two pairs of parallel sides and their opposite angles are congruent. Special types of parallelograms include rectangles, rhombi, and squares.
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Understanding quadrilaterals
- 2. A plane figure bounded by four line segments AB,BC,CD and DA is called a quadrilateral. A B D C
- 3. In geometry, a quadrilateral is a polygon with four sides and four vertices. Sometimes, the term quadrangle is used, for etymological symmetry with triangle, and sometimes tetragon for consistence with pentagon. There are over 9,000,000 quadrilaterals. Quadrilaterals are either simple (not self-intersecting) or complex (self-intersecting). Simple quadrilaterals are either convex or concave.
- 4. Parallelogram Trapezium Kite
- 6. 6 These figures are not polygons These figures are polygons Definition:A closed figure formed by line segments so that each segment intersects exactly two others, but only at their endpoints.
- 7. 7 Convex: No line containing a side of the polygon contains a point in its interior Concave: A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.
- 8. 8 Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length Irregular:Two sides (or two interior angles) are not congruent.
- 9. 9 3 sides Triangle 4 sides 5 sides 6 sides 7 sides 8 sides Nonagon Octagon Heptagon Hexagon Pentagon Quadrilateral 10 sides 9 sides 12 sides Decagon Dodecagon n sides n-gon
- 18. 18 polygons Classification by Sides with Flow Charts & Venn Diagrams triangles Scalene Equilateral Isosceles Triangle Polygon scalene isosceles equilateral
- 19. 19 polygons Classification by Angles with Flow Charts & Venn Diagrams triangles Right Equiangular Acute Triangle Polygon right acute equiangular Obtuse obtuse
- 20. • 2 sets of parallel sides • 2 sets of equal sides • Opposite angles equal • Adjacent angles supplementary • Diagonals bisect each other • Diagonals form 2 congruent triangles Parallelogram
- 21. Types of Parallelograms *Rectangle I have all of the properties of the parallelogram PLUS - 4 right angles - diagonals congruent
- 22. *Rhombus I have all of the properties of the parallelogram PLUS - 4 congruent sides - diagonals bisect angles - diagonals perpendicular
- 23. *Square Hey, look at me! I have all of the properties of the parallelogram AND the rectangle AND the rhombus. I have it all!
- 24. Is a square a rectangle? • Some people define categories exclusively, so that a rectangle is a quadrilateral with four right angles that is not a square. • This is appropriate for everyday use of the words, as people typically use the less specific word only when the more specific word will not do. • Generally a rectangle which isn't a square is an oblong.
- 25. • But in mathematics, it is important to define categories inclusively, so that a square is a rectangle. • Inclusive categories make statements of theorems shorter, by eliminating the need for tedious listing of cases. • For example, the visual proof that vector addition is commutative is known as the "parallelogram diagram". • If categories were exclusive it would have to be known as the "parallelogram (or rectangle or rhombus or square) diagram"!
- 26. Trapezium I have only one set of parallel sides. [The median of a trapezium is parallel to the bases and equal to one-half the sum of the bases.] Trapezoid Regular Trapezoid
- 27. • It has two pairs of sides. Each pair is made up of adjacent sides (the sides meet) that are equal in length. • The angles are equal where the pairs meet. • Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other. Kite
- 28. Cyclic quadrilateral: the four vertices lie on a circumscribed circle. Tangential quadrilateral: the four edges are tangential to an inscribed circle. Another term for a tangential polygon is inscriptible. Bicentric quadrilateral: both cyclic and tangential. Some other types of quadrilaterals
- 29. The sum of all four angles of a quadrilateral is 360 . . A B C D 1 2 3 4 6 5 Given: ABCD is a quadrilateral To Prove: Angle (A+B+C+D) =360 . Construction: Join diagonal BD
Editor's Notes
- Arun: Good morning to one and all .Today we are extremely happy to present a PowerPoint presentation on Understanding quadrilaterals. Now Jaswant of VIII-A and myself Arunprasad from VIII-A are going to present the ppt. Now Jaswant will explain about definition of a quadrilateral.