Presentazione sul tema: "Polygons, Quadrilaterals, Trapezes and Parallelogramms"— Transcript della presentazione:
1 Polygons, Quadrilaterals, Trapezes and Parallelogramms Geometry CLILPolygons, Quadrilaterals, Trapezes and Parallelogramms
2 GEOMETRY LESSONSEnglish Lessons in Geometry for Scuola Secondaria di I grado “ A. Brofferio” Asti, Class IIEBy Prof.ssa Anna Caruso (Engkish Teacher) and Silvia Giachin (Maths Teacher).We’re the members of the class II E composed of 27 students and we hope you enjoy our time together.THE TASKStudents are introduced to basic concepts of geometry.The classroom tasks is to experience the language use involved in geometry activities encouraging pupils’ practice of informal and formal mathematical vocabulary.
3 THE PARALLELOGRAMS: Definition and Properties QUADRILATERALSStudents learn to classify quadrilaterals, focusing on different types of parallelograms. They learn to investigate the relationships among rectangle, square, and rhombus as different types of parallelograms.THE PARALLELOGRAMS: Definition and PropertiesThe Parallelograms lesson of this course is designed to learn to identify parallelograms and the unique properties that belong to them. We will see the angles and the sides that are needed to prove that a certain shape is a parallelogramIDENTIFY AND DESCRIBE POLYGONS In this lesson, students will develop the academic language necessary to identify, describe, illustrate, classify and sort various polygons and figures that are not polygons. Which are concave and which are convex polygons.
4 POLYGONSA polygon is a plane shape with straight sides. They are made of straight lines, and the shape is closed (all the lines connect up).Polygon comes from Greek: poly means “many” and gon means “angle”The name tells you how many sides the shape has for example a triangle has 3 sides, a quadrilateral has four sides.This is a polygon (it has straight sides)This is not a polygon (it's open, not closed)This is not a polygon (it has a curve)
5 Concave or convexIn a convex polygon no internal angle can be more than 180, all the angles are convex.In a concave polygon internal angles are greater than 180, it has one or more concave angles.BBDCEACAEDFConcave polygonConvex polygon
6 The properties of polygons The sum of the angles outside a polygon is 360.A polygons is called regular polygon if it is equilateral and equiangular with equal angles. It means that all the sides and all the angles are congruent.A diagonal of a polygon is a line segment linking two non adjacent vertices.Equilateral polygon: a polygon with all its sides equal.=-Not a regular polygon: It’s got congruents angles, but the sides are different.
7 They are quadrilaterals because they’ve got 4 sides A quadrilateral is a plane shape, it has four sides, four angles and straight lines. It is closed: the lines join upQuadrilater means "four sides"QUAD means fourLATERAL means sidesThis isn’t a quadrilateral beacause it’s got only 3 sides; it’s a triangleThey are quadrilaterals because they’ve got 4 sides
8 THE PROPERTIES OF QUADRILATERALS Four sides;Sets of opposite sides are not consecutive sides;Sets of opposite angles (not adiacent angle) along the same side;You can have a quadrilateral only if the major sides is minor than the sum of the other three sides.ABCD4BC < AB+AD+DCBD and AC are diagonalsA+B+C+D= 360°2p= AB+BC+CD+AD3122143
9 The vertex is the end point of 2 or more rays or line segments. QUADRILATERALA quadrilateral can be changed in a rigid polygon by a DIAGONAL. The sum of the interior angles equals 360 degrees (°).A diagonal is a line segment drawn from a vertex of a quadrilateral to de opposite VERTEX.BABCDACDABCDThe vertex is the end point of 2 or more rays or line segments.123Sum= 360°= 360°4
10 TRAPEZIUMA quadrilateral is a plane figure with one pair of parallel sides, is called Trapezium.THE PROPERTIES ARE:The altitude (or height) of a trapezium is the perpendicular distance between two bases.The angles on the same side of an oblique side are called adjacent angles, such as A and D are supplementary.=ABCDD +A180°
11 Classification of Quadrilaterals 1. Trapeziums are a subset of quadrilateralsQTp
12 = TRAPEZIUM ELEMENTS Base= the 2 parallel lines are called bases: Oblique sides=ABCDMajor base (base greater)Minor base (smaller base)Base= the 2 parallel lines are called bases:Major base (base greater);Minor base (smaller base).Oblique side= the 2 non parallel lines are the oblique sides
13 TRAPEZIUM CLASSIFICATION An isoscel trapezium is a Trapezium with oblique sides equal(congruent);The major base adjacent angles are equal;The minor base adjacent angles are equal;The projections of the oblique sides on the major base are congruent;The diagonals are equal.BC=DA
14 _ = = _ PARALLELOGRAMS A parallelogram has opposite sides parallel. Parallelograms can have two heights (or altitudes).Opposite sides are congruent – equal lenght.Opposite angles are congruent.When the diagonals meet in the middle, they bisect each other.BC_==_DA
15 Classification of quadrilaterals 2. Parallelograms are a subset of trapeziums.QTpP
16 Rectangle Right angle is an internal angle which is equal to 90° A rectangle is a four side-shape with four right angles.A rectangle has two diagonals witch are line segments linking its opposite vertices.The two diagonals are congruent.Each diagonal bisects the other. The point where the diagonals intersect, divide search diagonal into two equal parts.Each side of the rectangle denotes the length relative to the other side, considered as base.Base and height can be called dimensions of the rectangle.CBDA
17 Set of quadrilaterals Q 3. Rectangles are a subset of parallelograms P TpPR
18 RhombusA Rhombus is a parallelogram with all four sides equal in length (congruent);Rhombus diagonals are perpendicular bisector;Diagonals are perpendicular.B==AD==C
19 Set of quadrilaterals Q 4. Rhombus are subset of parallelograms Tp P RoRe
20 Square A Rhombus where all angles are right angles is called square. A Rectangle with congruent sides is called squareSquares have congruent sides and four right anglesIn a square the diagonals are perpendicular, congruent and bisect the angles into two equal parts.BCAD
21 Set of quadrilaterals Q 5. Squares are an itersection set of rectcangles and rhombusQTpPRoQRe