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Mathematics

Published in: Mathematics
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  • Ashish K

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Triangle and its properties

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    MATHS CLASS - TRIANGLE AND ITS PROPERTIES
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    OVERVIEW Triangles Type of triangles Properties of triangle - Angle Sum Property - Relation Between Interior Angles and Angles - Pythagoras theorem Exterior
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    What do you see in this picture?
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    SWING What is the shape of swing? TRIANGULAR
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    Lets make a triangle
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    Today we will read bout the Triangle and its properties
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    What do these symbols mean? right angle SYMBOLS parallel to each other same length as each other parallel to each other, but not parallel with the sides with only one arrow same length as each other, but not the same length as the sides with only one dash
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    Triangles What are the names and properties of these triangles ? Isosceles: 2 sides the same length 2 angles the same Equilateral: All sides the same length All angles the same (600) Right-angled: Sides can be any length One angle 900 Scalene: All the sides are different lengths All the angles are different
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    Relation Between Interior Angles and b Exterior Angles E c d c ' Draw a line parallel to AB ' a=c (alternate interior angles) b=d (corresponding angles) therefore a+b = c+d
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    Angle Sum Property Proof that the internal angles in a triangle add up to 1800 b Add a line parallel to one of the sides Alternate angles are equal b Corresponding angles are equal The internal angles are now on a straight line and therefore must add up to 1800 (LINEAR PAIR)
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    Properties of Triangles Congruent: means all angles and lengths are the same. It can be a rotation b Which shapes are congruent? d i c
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    In this picture which type of triangle is this ? Right Angled Triangle h
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    Right Angled Triangle Hypotenuse h Perpendicular 1 Base
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    If the base of a right angled triangle is 4cm, perpendicular is 3cm then what will be the length of its Hypotenuse ? ' Cut the two squares of 3 cm and 4 cm respectively and place it as given below. ' Now make the square according to length of the hypotenuse. ' We can see that it becomes the square of 5 cm
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    Pythagoras Theorem Pythagoras Theorem In the right triangle, the square of the hypotenuse is equal to the sum of the squares of the othe two sidees. a2 + b2 = c2 We can say that in right angled triangle : b2 classteacher learning systems (Base)2 + (Perpendicular) 2 = (Hypotenuse)2
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    Now do these: c = 180 - (62+34) a = 180 - (80+30) x = 180-141 = 39 y = 180 - (58+39) z = 180-83 = 97 410 b = 180- = 85 Worksheet b 4 790 620 84 340 = 70 141 = 83 x z q c 570 580 p = 180 - (90+57) = 33 (vertically opposite q=57 angles are equal) (79+57) = 44 r = 180-
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    68 a c b 390 a = 180-90 = 90 180- (90+39) = 51 c = 180- (90+68) = 22 worksheet 460 17 d = 180 - (90+46) = 44 Think big triangle e = 180 - (90+44+17) = 29

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