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## Monday, July 20, 2020

### ATTRIBUTES OF SHAPES - WITH PROOF

SHAPES AND ITS PROPERTIES

There are different kinds of shapes. There are some features or qualities of a shape, and in this post we are going to discuss about it. You would discover the attributes of shapes with proof

PROPERTIES OF SQUARE

1. The square has four sides, and each of the side is equal

2. It has four angles, and each of the angle is of 90 degrees

3. The diagonals of the square are equal

4. The diagonals bisect each other at 90 degrees

PROPERTIES OF RECTANGLE

1. The rectangle has four sides, and its opposite sides are equal

2. It has four angles, and each of the angle is of 90 degrees

3. The diagonals of the rectangle are equal

4. The diagonals bisect each other at 90 degrees

PROPERTIES OF TRIANGLE

1. The triangle has three sides and three angles

2. The triangle may have all the 3 sides equal as in equilateral, it may have two sides equal as in isosceles and all of its sides may be unequal as in scalene triangle

3. The sum of two sides of a triangle is always greater than its third side

4. The sum of interior angles of a triangle is 180 degrees

PROPERTIES OF TRAPEZIUM

1. The trapezium has two parallel sides

2. It has also two non parallel sides

3.The length drawn in the mid point of trapezium is equal to half the sum of the parallel sides

4.The diagonals of the trapezium bisect each other

PROPERTIES OF RHOMBUS

1.The rhombus has four sides, and all the four sides are equal

2. The diagonals are perpendicular and bisect each other at right angle, and diagonals are not equal

3. The opposite angles are equal

4. The sum of two adjacent angles is equal to 180 degrees
PROPERTIES OF CIRCLE

1.The circle is round in shape, with no side

2. The longest chord of the circle is its diameter, which touches its two end points. The diameter always passes from the center of the circle

3. The radius is half of the diameter, and radius is the line from the center of the circle to any one end point. So radius also touches end point, but only one end point

4. Infinite number of diameter and radius can be drawn in the circle
 The diameters are AE, BF, CG and HD. Every diameter passes through the center of the circle which is O, and it touches two end points also. The radius are AO, BO, CO,DO, EO, FO, GO and HO. Hence radius also passes through the center of the circle, but it touches only one end point of the circle. ST, UV, WX and YZ also touches two end points of the circle, but any of them is not a diameter, since none of these pass through the center of the circle O. They are all chords only. The infinite number of radius and diameter can be drawn in the circle 5. If the radius of two circles is equal, then the circumference and area of both circles is also equal  If the radius of two circles is 14 cm, then the circumference of both circles is 2 X 22/7 X 14 = 88 cm, and area is 22/7 X 14 X 14 = 616 sq cm

6.The arc is a part or portion of the circle. The arc could be major or minor

7. The tangent is the exterior line outside the circle, which touches the circle at only one point . The radius is perpendicular to the tangent line at the point of tangency

PROPERTIES OF PENTAGON

1.The pentagon has five sides, and regular pentagon has all five sides equal

2. The sum of interior angles of a pentagon is 540, and hence each interior angle is of 108 degrees in regular pentagon

3. The pentagon has five diagonals, and each of the diagonal is not equal

PROPERTIES OF HEXAGON

1.The hexagon has six sides, and all the sides in regular hexagon is equal

2. The sum of interior angles of a hexagon is 720, and hence each interior angle is of 120 degrees in regular pentagon

3. It has nine diagonals, and each of the diagonal is not equal

PROPERTIES OF CUBE

1.There are six faces in a cube, and each face is a square, as all faces have equal length, breadth and height

2 .The cube has 12 edges and 8 vertices or corners

Its opposite faces are parallel

PROPERTIES OF CUBOID

1.The cuboid has 6 faces, and each face is a rectangle, because its length, breadth and height is unequal

2. It also has 12 edges and 8 vertices, as cube has

3. Its opposite faces are also parallel

PROPERTIES OF CYLINDER

1. The cylinder has 3 faces, one is rectangular and two are circular

2 It has two edges