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Angles and triangles
The document discusses angles and triangles, defining various types of angles and their properties, including complementary and supplementary angles. It covers the characteristics of triangles, notably that the sum of interior angles in a triangle equals 180°, and outlines types such as equilateral and isosceles triangles. Additionally, it introduces the Pythagorean theorem and the sine and cosine rules applicable to all triangles.
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Angles and triangles
- 1. Angles and Triangles -Prakash Kumar Sekar Prakash Kumar S
- 2. Angles An angleis the amount of rotation between two straight lines. Angles may be measured either in degrees or in radians. If a circle is divided into 360 equal parts, then each part is called 1 degree and is written as 1◦ 1 revolution = 360◦ Prakash Kumar S
- 3. Any angle between0◦ and 90◦ is called an acute angle. An angle equal to 90◦ is called a right angle. Any angle between 90◦ and 180◦ is called an obtuse angle. Any angle greater than 180◦ and less than 360◦ is called a reflex angle. An angle of 180◦ lies on a straight line. If two angles add up to 90◦ they are called complementary angles. If two angles add up to 180◦ they are called supplementary angles. Prakash Kumar S
- 4. Finding Unknown Angles a= c, b = d, e = g and f = h. Such pairs of angles are called vertically opposite angles. (b) a = e, b = f , c = g and d = h. Such pairs of angles are called corresponding angles. (c) c = e and b = h. Such pairs of angles are called alternate angles. (d) b + e = 180◦ and c + h = 180◦. Such pairs of angles are called interior angles.Prakash Kumar S
- 5. Radians and Minutes 1 degree = 60 minutes 50’ + 40’ = ? θ = s/r = 2πr/r = 2π 2 = 360 = 180 1 radian = 180/ 2 radian = ? Prakash Kumar S
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- 7. Find alpha X +Y = alpha X + 137 = 180 ( interior angles ) Y = 16 (corresponding angles) x y Prakash Kumar S
- 8. Triangle A triangleis a figure enclosed by three straight lines. The sum of the three angles of a triangle is equal to 180◦ 30 + 75 + 75 = 180 Prakash Kumar S
- 9. Types of Triangles Anequilateral triangle is one in which all the sides and all the angles are equal An isosceles triangle is one in which two angles and two sides are equal. Prakash Kumar S
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- 12. Finding Angles, Sidesand Distances Prakash Kumar S
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- 15. Find DB Similar Triangles 9/(9+6)= x/10 X = 6 Prakash Kumar S
- 16. The theorem ofPythagoras In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Prakash Kumar S
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- 19. Find this onyour Own Prakash Kumar S A surveyor measures the angle of elevation of the top of a perpendicular building as 19◦. He moves 120m nearer to the building and finds the angle of elevation is now 47◦. Determine the height of the building
- 20. Sine and CosineRule They are applicable for all type of triangle Sine Rule a/sinA = b/sinB = c/sinC Cos Rule a^2 = b^2 + C^2 – 2bc*cosA Prakash Kumar S
- 21. Thank You By PrakashKumar S Prakash Kumar S