MATHSXSTD10/10-PLANES &GEOMETRIC CONSTRUCTION : MATHSXSTD10/10-PLANES &GEOMETRIC CONSTRUCTION BY MANJULA
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PLANES-CONCEPTS : PLANES-CONCEPTS TO UNDERSTAND PLANE WE NEED TO KNOW THE FOLLOWING
1)DENSELY PACKED INFINITE SET OF POINTS IS CALLED A LINE
2) A LINE PARALLEL TO PLUMB LINE IS CALLED A VERTICAL LINE
3)A LINE PERPENDICULAR TO A VERTICAL LINE IS CALLED HORIZONTAL LINE
4) A LINE THAT IS NEITHER VERTICAL NOR HORIZONTAL IS CALLED OBLIQUE LINE
5)DENSELY PACKED SET OF POINTS WITH NO THICKNESS BUT HAVING AN AREA IS CALLED SURFACE
PLANES-CONTD : PLANES-CONTD 6)A SURFACE HAS NO THICKNESS BUT HAS AREA
7)A SURFACE IS A SET OF INFINITE NUMBER OF POINTS
8)WHEN THREE NON-COLLINEAR POINTS ON A SURFACE ARE JOINED IN PARTS, IF ANY OF TWO LINES ARE CURVED THEN IT IS CALLED CURVED SURFACE
9)WHEN THREE NON-COLLINEAR POINTS ON A SURFACE ARE JOINED IN PARTS, IF ALL THE THREE LINES ARE STRAIGHT LINES THEN SUCH SURFACE WILL BE FLAT AND CALLED A PLANE
10)THREE NON-COLLINEAR POINTS DETERMINE A PLANE
PLANES-PROPERTIES : PLANES-PROPERTIES THE POINTS LYING IN A PLANE ARE CALLED COPLANAR POINTS
THE LINES JOINING ANY TWO POINTS IN A PLANE IS ALWAYS A STRAIGHT LINE AND LIES WHOLLY ON THE PLANE
LINES LYING IN THE SAME PLANE ARE CALLED COPLANAR PLANES
HORIZONTAL,VERTICAL,OBLIQUE PLANCES ARE THE THREE KINDS OF PLANES
A PLANE WHICH IS PERPENDICULAR TO A PLUMB LINE IS CALLED A HORIZONTAL PLANE EX: SURFACE OF WATER IN A VESSEL
A PLANE PASSING THROUGH A PLUMB LINE IS CALLED VERTICAL PLANE EX: WALLS OF A ROOM
A PLANCE WHICH IS NEITHER HORIZONTAL NOR VERTICAL IS CALLED OBLIQUE PLANE EX : LATERAL SIDES OF A PYRAMID
ALL LINES IN A HORIZONTAL ARE HORIZONTAL
PLANCES-PROPERTIES : PLANCES-PROPERTIES LINES IN A VERTICAL PLANE MAY BE HORIZONTAL, VERTICAL OR OBLIQUE
LINES IN AN OBLIQUE PLANE MAY BE HORIZONTAL OR VERTICAL BUT CAN NEVER BE VERTICAL
A HORIZONTAL PLANCE CONTAINS HORIZONTAL LINES ONLY
A VERTICAL PLANCE CONTAINS VETICAL LINES, HORIZONTAL LINES AND OBLIQUE LINES
AN OBLIQUE PLANE CONTAINS HORIZONTAL LINES AND OBLIQUE LINES BUT NOT VERTICAL LINES
TWO NON-INTERSECTING PLANES ARE CALLED PARALLEL PLANES
TWO HORIZONTAL PLANES ARE ALWAYS PARALLEL
PLANES-PROPERTIES : PLANES-PROPERTIES TWO VERTICAL AND OBLUQUE PLANCS MAY OR MAY NOT BE PARALLEL
WHEN TWO PLANES INTERSECT ALONG A LINE, IT IS CALLED THE LINE INTERSECTION OF THE PLANES, WHICH MAY BE HORIZONTAL, VERTICAL OR OBLIQUE ACCORDING TO THE KINDS OF PLANES INTERSECTING
TWO HORIZONTAL PLANES NEVER INTERSECT
IF TWO VERTICAL PLANES INTERSECT, THEY DO SO ALONG A VERTICAL LINE
IF ANY PLANCE INTERSECT A HORIZONTAL PLANCES THENS THE LINE INTERSECTION IS HORIZONTAL LINE
THE FLOOR AND WALL OF A ROOM INTERESECT ALONG A HORIZONTAL LINE
PLANES-PROPERTIES : PLANES-PROPERTIES THE HORIZONTAL B ASE AND A LATERAL FACE OF A PYRAMID INTERSECT ALONG A HORIZONTAL LINE
IF AN VERTICAL PLANE AND AN OBLIQUE PLANE INTERSECT THEY DO SO ALONG A HORIZONTAL LINE OR AN OBLIQUE LINE
THE ANGLE BETWEEN TWO INTERSECTING PLANCES IS CALLED DIHEDRYAL ANGLE
IF THE ANGLE BETWEEN TWO INTERSECTING PLANCES IS A RIGHT ANGLE THEN THE PLANCES ARE SAID TO BE PERPENDICULAR PLANES.
TWO VERTICAL PLANES MAY BE PERPENDICULAR TO ONE ANOTHER (TWO ADJUCENT WALLS OF A ROOM)
TWO OBLIQUE PLANES MAY BE PERPENDICULAR TO ONE ANOTHER (A CUBE MADE TO STAND ON AN EDGE)
PLANCES-PROPERTIES : PLANCES-PROPERTIES TWO HORIZONTAL PLANES ARE NEVER PERPENDICULAR(FLOOR AND ROOF OF A ROOM)
ANY PLANE PERPENDICULAR TO A HORIZONTAL PLANCE IS VERTICAL(FLOOR AND WALL OF A ROOM)
ANY PLANE PERPENDICULAR TO A VE TICAL IS HORIZONTAL, VERTICAL OR OBLIQUE(WALL AND FLOOR OF A ROOM)
TWO LINES IN SPACE WHICH ARE COPLANAR ARE CALLED SKEW LINES
FOUR VERTICAL PLANCES ARE THERE IN A CUBE
GEOMETRIC CONSTRUCTIONS : GEOMETRIC CONSTRUCTIONS A STRAIGHT LINE WHICH IS A TANGENT TO TWO CIRCLES IS A DIRECT TANGENT
IF THE CENTRE OF THE CIRCLE LIE ON SAME SIDE OF THE COMMON TANGENT THEN THE TANGENT IS CALLED DIRECT COMMON TANGENT
IF THE CENTRE OF THE CIRCLE LIE ON OTHER SIDE OF THE COMMON TANGENT THEN THE TANGENT IS CALLED TRANSEVERSE COMMON TANGENT
IF THE CIRCLES ARE INTERESECTING THEN NO TRANSVERSE COMMON TANGENT CAN BE DRAWN ON TO THE CIRCLES.
IF THE CIRCLES ARE CONCENTRIC, THEN NO COMMON TANGENT CAN BE DRAWN
IF THE CIRCLES ARE NOT TOUCHING BUT ONE CIRCLE IS INSIDE THE OTHER, THEN NO COMMON TANGENT CAN BE DRAWN