1. CONTENT and LANGUAGE INTEGRATED LEARNING You learn content….. MATHS You practice language in a specific context…..

2. Let’s talk about…. ANGLES What is an angle? Angle: the inclination to one another of two straight lines that meet. The point at which two lines meet is called the vertex of the angle (plural: vertices); the two straight lines are called sides

3. Look at these different types of angles and remember their names: Right angle: measures 90 degrees (its sides are perpendicular) Straight angle: measures 180 degrees (its sides lie on the same straight line) a straight angle equals two right angles

4. Obtuse angles: measure more than 90° but less than 180° (i.e. is greater than a right angle but less than a right one) Acute angles: measure less than 90° (i.e. less than a right angle)

5. Angles are complementary (or complements of one another) if together they equal a right angle. Angles are supplementary (or supplements of one another) if together they equal a straight angle (  and  are also adjacent)   

6. TRIANGLES In a triangle: we use capital letters for the vertices we name the opposite side of each vertex with the same letter in small letters. we name the angles with Greek letters (  ) corresponding to the vertices A, B, C A triangle is a polygon with three sides and three angles The triangle on the right is the ABC triangle (e.g. side c is the opposite side of angle  ; angles  and  are adjacent to side c) C    B A a c b

7. Look at these properties of triangles: there is a connection between the length of the sides and the size of the angles: The side opposite to the bigger angle is longer, the same with the small one The sum of two sides is always bigger than the remaining side The three angles always add to 180°

8. Activity: Complete : (refer to ABC triangle) a < c  ………… < ……….. a < … + … ; b < … + …  = ………° C    B A a c b

9. How many types of TRIANGLES? There are three special names given to triangles that tell how many sides (or angles) are equal: scalene, isosceles, equilateral (  classification of triangles according to sides) Triangles can also have names that tell you what types of angles are inside: acute, right, obtuse (  classification of triangles according to angles)

10. Types of triangles By their sides Equilateral triangle A triangle having all three sides of equal length Isosceles triangle A triangle having two sides of the same length Scalene triangle A triangle having all three sides of different length By their angles Acute triangle A triangle having all acute angles Right triangle (right angled t.) A triangle having a right angle Obtuse Triangle A triangle having an obtuse angle

11. Now answer to these questions: a)Does a triangle with two obtuse angles exist? b)What is the size of the angles in an equilateral triangle? c)If the vertex angle ( = the angle which is opposite to the base) of an isosceles triangle is 100°, what is the size of the remaining angles? How can you classify the triangle in another way? d) What type of triangle is the grey one? Example of answer: “the grey triangle is …………… because it has an ……… angle; it has also two …… sides, so/therefore it is an ……………… triangle

12. RIGHT ANGLED TRIANGLES The side opposite to the right angle is called “hypotenuse” and it is the longest side The other two sides are called “legs” the hypotenuse is …. the legs are …… and …… The inner acute angles add to 90, so they are ………………….

13. The right angled triangle is one of the most useful shapes in all of mathematics! A right triangle can be isosceles; it is called isosceles right angled triangle  T he size of the acute angles in this type of right triangle is always ……… ° (try to explain why)  We can obtain two equal isosceles right angled triangle if we draw a diagonal of a square (in another way: a square can be divided by a diagonal into two isosceles right triangles, that are equal OR: a square is formed by two equal isosceles right triangles, joined by the hypoyhenuse)

14. Next lesson: The Pythagorean Theorem!!

15. NAMING POLYGONS: Look at these shapes and find the right name among those written on the bottom of the slide

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