Polygons, Quadrilaterals, Trapezes and Parallelogramms Geometry CLIL Polygons, Quadrilaterals, Trapezes and Parallelogramms

GEOMETRY LESSONS English Lessons in Geometry  for Scuola Secondaria di I grado “ A. Brofferio” Asti, Class IIE 2015-16 By Prof.ssa Anna Caruso (English Teacher) And Prof.ssa 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 TASK Students 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.

THE PARALLELOGRAMS: Definition and Properties QUADRILATERALS Students 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 Properties The 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 parallelogram IDENTIFY 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.

POLYGONS A 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)

Concave or convex In 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. B B D C E A C A E D F Concave polygon Convex polygon

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.

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 up Quadrilater means "four sides" QUAD means four LATERAL means sides This isn’t a quadrilateral beacause it’s got only 3 sides; it’s a triangle They are quadrilaterals because they’ve got 4 sides

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. A B C D 4 BC < AB+AD+DC BD and AC are diagonals A+B+C+D= 360° 2p= AB+BC+CD+AD 3 1 2 2 1 4 3

The vertex is the end point of 2 or more rays or line segments. QUADRILATERAL A 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. B A B C D A C D A B C D The vertex is the end point of 2 or more rays or line segments. 1 2 3 Sum= 360° 1+2+3+4= 360° 4

TRAPEZIUM A 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. = A B C D D + A 180°

= TRAPEZIUM ELEMENTS Base= the 2 parallel lines are called bases: Oblique sides = A B C D Major 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

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. B C = D A

Classification of Quadrilaterals 1. Trapeziums are a subset of quadrilaterals Q Tp

_ = = _ 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. B C _ = = _ D A

Classification of quadrilaterals 2. Parallelograms are a subset of trapeziums. Q Tp P

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. C B D A

Rhombus A Rhombus is a parallelogram with all four sides equal in length (congruent); Opposite angles are equal; Rhombus diagonals are perpendicular bisector; Diagonals are perpendicular. B = = A D = = C

Set of quadrilaterals Q 4. Rhombus are subset of parallelograms Tp P Ro Re

Square A Rhombus where all angles are right angles is called square. A Rectangle with congruent sides is called square Squares have congruent sides and four right angles In a square the diagonals are perpendicular, congruent and bisect the angles into two equal parts. B C A D

Set of quadrilaterals Q 5. Squares are an intersection set of rectangles and rhombus Q Tp P Ro Q Re